A Tour of Representation Theory

A Tour of Representation Theory

Author: Martin Lorenz

Publisher: American Mathematical Soc.

Published: 2018

Total Pages: 654

ISBN-13: 1470436809

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Representation theory investigates the different ways in which a given algebraic object--such as a group or a Lie algebra--can act on a vector space. Besides being a subject of great intrinsic beauty, the theory enjoys the additional benefit of having applications in myriad contexts outside pure mathematics, including quantum field theory and the study of molecules in chemistry. Adopting a panoramic viewpoint, this book offers an introduction to four different flavors of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is devoted to each of these areas and they are all treated in sufficient depth to enable and hopefully entice the reader to pursue research in representation theory. The book is intended as a textbook for a course on representation theory, which could immediately follow the standard graduate abstract algebra course, and for subsequent more advanced reading courses. Therefore, more than 350 exercises at various levels of difficulty are included. The broad range of topics covered will also make the text a valuable reference for researchers in algebra and related areas and a source for graduate and postgraduate students wishing to learn more about representation theory by self-study.


Book Synopsis A Tour of Representation Theory by : Martin Lorenz

Download or read book A Tour of Representation Theory written by Martin Lorenz and published by American Mathematical Soc.. This book was released on 2018 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representation theory investigates the different ways in which a given algebraic object--such as a group or a Lie algebra--can act on a vector space. Besides being a subject of great intrinsic beauty, the theory enjoys the additional benefit of having applications in myriad contexts outside pure mathematics, including quantum field theory and the study of molecules in chemistry. Adopting a panoramic viewpoint, this book offers an introduction to four different flavors of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is devoted to each of these areas and they are all treated in sufficient depth to enable and hopefully entice the reader to pursue research in representation theory. The book is intended as a textbook for a course on representation theory, which could immediately follow the standard graduate abstract algebra course, and for subsequent more advanced reading courses. Therefore, more than 350 exercises at various levels of difficulty are included. The broad range of topics covered will also make the text a valuable reference for researchers in algebra and related areas and a source for graduate and postgraduate students wishing to learn more about representation theory by self-study.


Representation

Representation

Author: Stuart Hall

Publisher: SAGE

Published: 1997-04-08

Total Pages: 422

ISBN-13: 9780761954323

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This broad-ranging text offers a comprehensive outline of how visual images, language and discourse work as `systems of representation'. Individual chapters explore: representation as a signifying practice in a rich diversity of social contexts and institutional sites; the use of photography in the construction of national identity and culture; other cultures in ethnographic museums; fantasies of the racialized `Other' in popular media, film and image; the construction of masculine identities in discourses of consumer culture and advertising; and the gendering of narratives in television soap operas.


Book Synopsis Representation by : Stuart Hall

Download or read book Representation written by Stuart Hall and published by SAGE. This book was released on 1997-04-08 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This broad-ranging text offers a comprehensive outline of how visual images, language and discourse work as `systems of representation'. Individual chapters explore: representation as a signifying practice in a rich diversity of social contexts and institutional sites; the use of photography in the construction of national identity and culture; other cultures in ethnographic museums; fantasies of the racialized `Other' in popular media, film and image; the construction of masculine identities in discourses of consumer culture and advertising; and the gendering of narratives in television soap operas.


Resemblance and Representation

Resemblance and Representation

Author: Ben Blumson

Publisher: Open Book Publishers

Published: 2014-09-21

Total Pages: 222

ISBN-13: 1783740728

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It’s a platitude – which only a philosopher would dream of denying – that whereas words are connected to what they represent merely by arbitrary conventions, pictures are connected to what they represent by resemblance. The most important difference between my portrait and my name, for example, is that whereas my portrait and I are connected by my portrait’s resemblance to me, my name and I are connected merely by an arbitrary convention. The first aim of this book is to defend this platitude from the apparently compelling objections raised against it, by analysing depiction in a way which reveals how it is mediated by resemblance. It’s natural to contrast the platitude that depiction is mediated by resemblance, which emphasises the differences between depictive and descriptive representation, with an extremely close analogy between depiction and description, which emphasises the similarities between depictive and descriptive representation. Whereas the platitude emphasises that the connection between my portrait and me is natural in a way the connection between my name and me is not, the analogy emphasises the contingency of the connection between my portrait and me. Nevertheless, the second aim of this book is to defend an extremely close analogy between depiction and description. The strategy of the book is to argue that the apparently compelling objections raised against the platitude that depiction is mediated by resemblance are manifestations of more general problems, which are familiar from the philosophy of language. These problems, it argues, can be resolved by answers analogous to their counterparts in the philosophy of language, without rejecting the platitude. So the combination of the platitude that depiction is mediated by resemblance with a close analogy between depiction and description turns out to be a compelling theory of depiction, which combines the virtues of common sense with the insights of its detractors.


Book Synopsis Resemblance and Representation by : Ben Blumson

Download or read book Resemblance and Representation written by Ben Blumson and published by Open Book Publishers. This book was released on 2014-09-21 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: It’s a platitude – which only a philosopher would dream of denying – that whereas words are connected to what they represent merely by arbitrary conventions, pictures are connected to what they represent by resemblance. The most important difference between my portrait and my name, for example, is that whereas my portrait and I are connected by my portrait’s resemblance to me, my name and I are connected merely by an arbitrary convention. The first aim of this book is to defend this platitude from the apparently compelling objections raised against it, by analysing depiction in a way which reveals how it is mediated by resemblance. It’s natural to contrast the platitude that depiction is mediated by resemblance, which emphasises the differences between depictive and descriptive representation, with an extremely close analogy between depiction and description, which emphasises the similarities between depictive and descriptive representation. Whereas the platitude emphasises that the connection between my portrait and me is natural in a way the connection between my name and me is not, the analogy emphasises the contingency of the connection between my portrait and me. Nevertheless, the second aim of this book is to defend an extremely close analogy between depiction and description. The strategy of the book is to argue that the apparently compelling objections raised against the platitude that depiction is mediated by resemblance are manifestations of more general problems, which are familiar from the philosophy of language. These problems, it argues, can be resolved by answers analogous to their counterparts in the philosophy of language, without rejecting the platitude. So the combination of the platitude that depiction is mediated by resemblance with a close analogy between depiction and description turns out to be a compelling theory of depiction, which combines the virtues of common sense with the insights of its detractors.


The Concept of Representation

The Concept of Representation

Author: Hanna F. Pitkin

Publisher: Univ of California Press

Published: 1967

Total Pages: 340

ISBN-13: 9780520021563

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This book arises out of Hannah Pitkin's doctoral dissertation and is considered by political scientists to be the gold standard in terms of a philosophical treatment of the subject. Pitkin covers the historical evolution of thinking about representation from the Greeks through the founding of the American republic highlighting diverse thinkers and politicians like Edmund Burke, Jeremy Bentham, and James Madison as well as more contemporary scholars like Robert Dahl and Charles Lindblom.


Book Synopsis The Concept of Representation by : Hanna F. Pitkin

Download or read book The Concept of Representation written by Hanna F. Pitkin and published by Univ of California Press. This book was released on 1967 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book arises out of Hannah Pitkin's doctoral dissertation and is considered by political scientists to be the gold standard in terms of a philosophical treatment of the subject. Pitkin covers the historical evolution of thinking about representation from the Greeks through the founding of the American republic highlighting diverse thinkers and politicians like Edmund Burke, Jeremy Bentham, and James Madison as well as more contemporary scholars like Robert Dahl and Charles Lindblom.


Representation

Representation

Author: Monica Brito Vieira

Publisher: John Wiley & Sons

Published: 2013-04-25

Total Pages: 174

ISBN-13: 0745658296

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What is representation? What does it mean when a politician represents citizens in government? How can citizens be represented beyond the boundaries of the nation-state? These are just some of the questions which will be answered by David Runciman and Mónica Brito Vieira as they explain why representation should be understood as one of the key concepts in modern politics. The first part of the book examines the historical roots of the concept of representation, from its origins in ancient Rome through to its role in the revolutionary politics of the modern world. The second looks at different varieties of representation – in law as well as politics. The final part asks how the concept of representation can help us think creatively about current and future challenges facing the world. Representation is too often treated as a secondary or qualifying idea – as in the phrase ‘representative democracy’. This book argues that we have this the wrong way round. Representation is the foundational idea in almost all areas of our political life. Making sense of representation in its own terms is crucial for seeing why democracy functions the way it does, and for exploring how it might function differently.


Book Synopsis Representation by : Monica Brito Vieira

Download or read book Representation written by Monica Brito Vieira and published by John Wiley & Sons. This book was released on 2013-04-25 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is representation? What does it mean when a politician represents citizens in government? How can citizens be represented beyond the boundaries of the nation-state? These are just some of the questions which will be answered by David Runciman and Mónica Brito Vieira as they explain why representation should be understood as one of the key concepts in modern politics. The first part of the book examines the historical roots of the concept of representation, from its origins in ancient Rome through to its role in the revolutionary politics of the modern world. The second looks at different varieties of representation – in law as well as politics. The final part asks how the concept of representation can help us think creatively about current and future challenges facing the world. Representation is too often treated as a secondary or qualifying idea – as in the phrase ‘representative democracy’. This book argues that we have this the wrong way round. Representation is the foundational idea in almost all areas of our political life. Making sense of representation in its own terms is crucial for seeing why democracy functions the way it does, and for exploring how it might function differently.


Rape and Representation

Rape and Representation

Author: Lynn A. Higgins

Publisher: Columbia University Press

Published: 1993-07-15

Total Pages: 348

ISBN-13: 9780231514712

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Rape does not have to happen. The fact that it does--and in the United States a rape is reported every six minutes--indicates that we live in a rape-prone culture where rape or the threat of rape functions as a tool for enforcing sexual difference and hierarchy. Rape and Representation explores how cultural forms construct and reenforce social attitudes and behaviors that perpetuate sexual violence. The essays proceed from the observation that literature not only reflects but also contributes to what a society believes about itself. Fourteen essays by authors in the fields of English, American and African-American, German, African, Brazilian, Classical, and French literatures and film present a wide range of texts from different historical periods and cultures. Contributors demythologize patriarchal representation in literature and art in order to show how it makes rape seem natural and inevitable. Contributors include: the editors, John J. Winkler, Patricia Klindiest Joplin, Susan Winnett, Ellen Rooney, Coppélia Kahn, Eileen Julien, Marta Peixoto, Kathryn Gravdal, Carla Freccero, Nellie V. McKay, Nancy A. Jones, and Froma I. Zeitlin. Their work raises pressing--and often difficult--questions for feminist criticism.


Book Synopsis Rape and Representation by : Lynn A. Higgins

Download or read book Rape and Representation written by Lynn A. Higgins and published by Columbia University Press. This book was released on 1993-07-15 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rape does not have to happen. The fact that it does--and in the United States a rape is reported every six minutes--indicates that we live in a rape-prone culture where rape or the threat of rape functions as a tool for enforcing sexual difference and hierarchy. Rape and Representation explores how cultural forms construct and reenforce social attitudes and behaviors that perpetuate sexual violence. The essays proceed from the observation that literature not only reflects but also contributes to what a society believes about itself. Fourteen essays by authors in the fields of English, American and African-American, German, African, Brazilian, Classical, and French literatures and film present a wide range of texts from different historical periods and cultures. Contributors demythologize patriarchal representation in literature and art in order to show how it makes rape seem natural and inevitable. Contributors include: the editors, John J. Winkler, Patricia Klindiest Joplin, Susan Winnett, Ellen Rooney, Coppélia Kahn, Eileen Julien, Marta Peixoto, Kathryn Gravdal, Carla Freccero, Nellie V. McKay, Nancy A. Jones, and Froma I. Zeitlin. Their work raises pressing--and often difficult--questions for feminist criticism.


Introduction to Representation Theory

Introduction to Representation Theory

Author: Pavel I. Etingof

Publisher: American Mathematical Soc.

Published: 2011

Total Pages: 228

ISBN-13: 0821853511

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Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.


Book Synopsis Introduction to Representation Theory by : Pavel I. Etingof

Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.


Knowledge Representation and Reasoning

Knowledge Representation and Reasoning

Author: Ronald Brachman

Publisher: Morgan Kaufmann

Published: 2004-05-19

Total Pages: 414

ISBN-13: 1558609326

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Knowledge representation is at the very core of a radical idea for understanding intelligence. This book talks about the central concepts of knowledge representation developed over the years. It is suitable for researchers and practitioners in database management, information retrieval, object-oriented systems and artificial intelligence.


Book Synopsis Knowledge Representation and Reasoning by : Ronald Brachman

Download or read book Knowledge Representation and Reasoning written by Ronald Brachman and published by Morgan Kaufmann. This book was released on 2004-05-19 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knowledge representation is at the very core of a radical idea for understanding intelligence. This book talks about the central concepts of knowledge representation developed over the years. It is suitable for researchers and practitioners in database management, information retrieval, object-oriented systems and artificial intelligence.


Representation and Citizenship

Representation and Citizenship

Author: Richard Marback

Publisher: Series in Citizenship

Published: 2016

Total Pages: 0

ISBN-13: 9780814342466

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Concern with representation figures inescapably in the study of citizenship. From the initial formulations of a notion of citizenship in ancient Greece, in which citizens were persons charged with representing the interests of the city-state, concern about who and what gets represented, as well as how and why those people and things get represented, has been central in formulas describing the citizen's relationship to a political community. Since the seventeenth century, the tension between citizens as representatives of the interests of the state and the state as representative of the interests of its citizens has found both practical and theoretical elaborations in understandings and exercises of citizenship. Today, the concept of representation resonates widely within citizenship studies, and its general ambiguity gives expression to many of the key issues of community membership, creating in this way a critical vocabulary through which those issues can be expressed. It is this vocabulary of representation that this book examines. Representation and Citizenship is a collection of seven essays that speak to the pull in citizenship studies between founding beliefs that organize political communities and claims for multicultural and cosmopolitan expansions of those community beliefs. Each contributor takes a stance on supporting either founding beliefs or multicultural values, yet none are at the exclusion of the other. The essays explore the relevance of specific national contexts, including the United States, Canada, and Korea, and as a whole, argue that the tension between inclusion and exclusion retains significance for any assertion of what citizenship means. The audience for this book includes, but is not limited to, students and scholars in citizenship studies, history, law, political science, and social science, especially those interested in issues of patriotism and multiculturalism.


Book Synopsis Representation and Citizenship by : Richard Marback

Download or read book Representation and Citizenship written by Richard Marback and published by Series in Citizenship. This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concern with representation figures inescapably in the study of citizenship. From the initial formulations of a notion of citizenship in ancient Greece, in which citizens were persons charged with representing the interests of the city-state, concern about who and what gets represented, as well as how and why those people and things get represented, has been central in formulas describing the citizen's relationship to a political community. Since the seventeenth century, the tension between citizens as representatives of the interests of the state and the state as representative of the interests of its citizens has found both practical and theoretical elaborations in understandings and exercises of citizenship. Today, the concept of representation resonates widely within citizenship studies, and its general ambiguity gives expression to many of the key issues of community membership, creating in this way a critical vocabulary through which those issues can be expressed. It is this vocabulary of representation that this book examines. Representation and Citizenship is a collection of seven essays that speak to the pull in citizenship studies between founding beliefs that organize political communities and claims for multicultural and cosmopolitan expansions of those community beliefs. Each contributor takes a stance on supporting either founding beliefs or multicultural values, yet none are at the exclusion of the other. The essays explore the relevance of specific national contexts, including the United States, Canada, and Korea, and as a whole, argue that the tension between inclusion and exclusion retains significance for any assertion of what citizenship means. The audience for this book includes, but is not limited to, students and scholars in citizenship studies, history, law, political science, and social science, especially those interested in issues of patriotism and multiculturalism.


Art and Representation

Art and Representation

Author: John Willats

Publisher: Princeton University Press

Published: 1997

Total Pages: 428

ISBN-13: 9780691087375

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In Art and Representation, John Willats presents a radically new theory of pictures. To do this, he has developed a precise vocabulary for describing the representational systems in pictures: the ways in which artists, engineers, photographers, mapmakers, and children represent objects. His approach is derived from recent research in visual perception and artificial intelligence, and Willats begins by clarifying the key distinction between the marks in a picture and the features of the scene that these marks represent. The methods he uses are thus closer to those of a modern structural linguist or psycholinguist than to those of an art historian. Using over 150 illustrations, Willats analyzes the representational systems in pictures by artists from a wide variety of periods and cultures. He then relates these systems to the mental processes of picture production, and, displaying an impressive grasp of more than one scholarly discipline, shows how the Greek vase painters, Chinese painters, Giotto, icon painters, Picasso, Paul Klee, and David Hockney have put these systems to work. But this book is not only about what systems artists use but also about why artists from different periods and cultures have used such different systems, and why drawings by young children look so different from those by adults. Willats argues that the representational systems can serve many different functions beyond that of merely providing a convincing illusion. These include the use of anomalous pictorial devices such as inverted perspective, which may be used for expressive reasons or to distance the viewer from the depicted scene by drawing attention to the picture as a painted surface. Willats concludes that art historical changes, and the developmental changes in children's drawings, are not merely arbitrary, nor are they driven by evolutionary forces. Rather, they are determined by the different functions that the representational systems in pictures can serve. Like readers of Ernst Gombrich's famous Art and Illusion (still available from Princeton University Press), on which Art and Representation makes important theoretical advances, or Rudolf Arnheim's Art and Visual Perception, Willats's readers will find that they will never again return to their old ways of looking at pictures.


Book Synopsis Art and Representation by : John Willats

Download or read book Art and Representation written by John Willats and published by Princeton University Press. This book was released on 1997 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Art and Representation, John Willats presents a radically new theory of pictures. To do this, he has developed a precise vocabulary for describing the representational systems in pictures: the ways in which artists, engineers, photographers, mapmakers, and children represent objects. His approach is derived from recent research in visual perception and artificial intelligence, and Willats begins by clarifying the key distinction between the marks in a picture and the features of the scene that these marks represent. The methods he uses are thus closer to those of a modern structural linguist or psycholinguist than to those of an art historian. Using over 150 illustrations, Willats analyzes the representational systems in pictures by artists from a wide variety of periods and cultures. He then relates these systems to the mental processes of picture production, and, displaying an impressive grasp of more than one scholarly discipline, shows how the Greek vase painters, Chinese painters, Giotto, icon painters, Picasso, Paul Klee, and David Hockney have put these systems to work. But this book is not only about what systems artists use but also about why artists from different periods and cultures have used such different systems, and why drawings by young children look so different from those by adults. Willats argues that the representational systems can serve many different functions beyond that of merely providing a convincing illusion. These include the use of anomalous pictorial devices such as inverted perspective, which may be used for expressive reasons or to distance the viewer from the depicted scene by drawing attention to the picture as a painted surface. Willats concludes that art historical changes, and the developmental changes in children's drawings, are not merely arbitrary, nor are they driven by evolutionary forces. Rather, they are determined by the different functions that the representational systems in pictures can serve. Like readers of Ernst Gombrich's famous Art and Illusion (still available from Princeton University Press), on which Art and Representation makes important theoretical advances, or Rudolf Arnheim's Art and Visual Perception, Willats's readers will find that they will never again return to their old ways of looking at pictures.