Invariant Theory and Superalgebras

Invariant Theory and Superalgebras

Author: Frank D. Grosshans

Publisher: American Mathematical Soc.

Published: 1987-12-31

Total Pages: 106

ISBN-13: 0821807196

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This book brings the reader to the frontiers of research in some topics in superalgebras and symbolic method in invariant theory. Superalgebras are algebras containing positively-signed and negatively-signed variables. One of the book's major results is an extension of the standard basis theorem to superalgebras. This extension requires a rethinking of some basic concepts of linear algebra, such as matrices and coordinate systems, and may lead to an extension of the entire apparatus of linear algebra to ``signed'' modules. The authors also present the symbolic method for the invariant theory of symmetric and of skew-symmetric tensors. In both cases, the invariants are obtained from the symbolic representation by applying what the authors call the umbral operator. This operator can be used to systematically develop anticommutative analogs of concepts of algebraic geometry, and such results may ultimately turn out to be the main byproduct of this investigation. While it will be of special interest to mathematicians and physicists doing research in superalgebras, invariant theory, straightening algorithms, Young bitableaux, and Grassmann's calculus of extension, the book starts from basic principles and should therefore be accessible to those who have completed the standard graduate level courses in algebra and/or combinatorics.


Book Synopsis Invariant Theory and Superalgebras by : Frank D. Grosshans

Download or read book Invariant Theory and Superalgebras written by Frank D. Grosshans and published by American Mathematical Soc.. This book was released on 1987-12-31 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings the reader to the frontiers of research in some topics in superalgebras and symbolic method in invariant theory. Superalgebras are algebras containing positively-signed and negatively-signed variables. One of the book's major results is an extension of the standard basis theorem to superalgebras. This extension requires a rethinking of some basic concepts of linear algebra, such as matrices and coordinate systems, and may lead to an extension of the entire apparatus of linear algebra to ``signed'' modules. The authors also present the symbolic method for the invariant theory of symmetric and of skew-symmetric tensors. In both cases, the invariants are obtained from the symbolic representation by applying what the authors call the umbral operator. This operator can be used to systematically develop anticommutative analogs of concepts of algebraic geometry, and such results may ultimately turn out to be the main byproduct of this investigation. While it will be of special interest to mathematicians and physicists doing research in superalgebras, invariant theory, straightening algorithms, Young bitableaux, and Grassmann's calculus of extension, the book starts from basic principles and should therefore be accessible to those who have completed the standard graduate level courses in algebra and/or combinatorics.

Invariant Theory

Invariant Theory

Author: T.A. Springer

Publisher: Springer

Published: 2006-11-14

Total Pages: 118

ISBN-13: 3540373705

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Book Synopsis Invariant Theory by : T.A. Springer

Download or read book Invariant Theory written by T.A. Springer and published by Springer. This book was released on 2006-11-14 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Classical Invariant Theory

Classical Invariant Theory

Author: Peter J. Olver

Publisher: Cambridge University Press

Published: 1999-01-13

Total Pages: 308

ISBN-13: 9780521558211

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The book is a self-contained introduction to the results and methods in classical invariant theory.


Book Synopsis Classical Invariant Theory by : Peter J. Olver

Download or read book Classical Invariant Theory written by Peter J. Olver and published by Cambridge University Press. This book was released on 1999-01-13 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a self-contained introduction to the results and methods in classical invariant theory.

Invariant Theory

Invariant Theory

Author: Mara D. Neusel

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 326

ISBN-13: 0821841327

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This book presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples and applications to physics, engineering, numerical analysis, combinatorics, coding theory, and graph theory. A wide selection of exercises and suggestions for further reading makes the book appropriate for an advanced undergraduate or first-year graduate level course.


Book Synopsis Invariant Theory by : Mara D. Neusel

Download or read book Invariant Theory written by Mara D. Neusel and published by American Mathematical Soc.. This book was released on 2007 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples and applications to physics, engineering, numerical analysis, combinatorics, coding theory, and graph theory. A wide selection of exercises and suggestions for further reading makes the book appropriate for an advanced undergraduate or first-year graduate level course.

Invariant Theory, Old and New

Invariant Theory, Old and New

Author: Jean Alexandre Dieudonné

Publisher:

Published: 1971

Total Pages: 104

ISBN-13:

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Book Synopsis Invariant Theory, Old and New by : Jean Alexandre Dieudonné

Download or read book Invariant Theory, Old and New written by Jean Alexandre Dieudonné and published by . This book was released on 1971 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Homogeneous Spaces and Invariant Theory

Algebraic Homogeneous Spaces and Invariant Theory

Author: Frank D. Grosshans

Publisher: Springer

Published: 2006-11-14

Total Pages: 158

ISBN-13: 3540696172

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The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years. This book is an exposition of several related topics including observable subgroups, induced modules, maximal unipotent subgroups of reductive groups and the method of U-invariants, and the complexity of an action. Much of this material has not appeared previously in book form. The exposition assumes a basic knowledge of algebraic groups and then develops each topic systematically with applications to invariant theory. Exercises are included as well as many examples, some of which are related to geometry and physics.


Book Synopsis Algebraic Homogeneous Spaces and Invariant Theory by : Frank D. Grosshans

Download or read book Algebraic Homogeneous Spaces and Invariant Theory written by Frank D. Grosshans and published by Springer. This book was released on 2006-11-14 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years. This book is an exposition of several related topics including observable subgroups, induced modules, maximal unipotent subgroups of reductive groups and the method of U-invariants, and the complexity of an action. Much of this material has not appeared previously in book form. The exposition assumes a basic knowledge of algebraic groups and then develops each topic systematically with applications to invariant theory. Exercises are included as well as many examples, some of which are related to geometry and physics.

Invariant Theory of Finite Groups

Invariant Theory of Finite Groups

Author: Mara D. Neusel

Publisher: American Mathematical Soc.

Published: 2010-03-08

Total Pages: 384

ISBN-13: 0821849816

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The questions that have been at the center of invariant theory since the 19th century have revolved around the following themes: finiteness, computation, and special classes of invariants. This book begins with a survey of many concrete examples chosen from these themes in the algebraic, homological, and combinatorial context. In further chapters, the authors pick one or the other of these questions as a departure point and present the known answers, open problems, and methods and tools needed to obtain these answers. Chapter 2 deals with algebraic finiteness. Chapter 3 deals with combinatorial finiteness. Chapter 4 presents Noetherian finiteness. Chapter 5 addresses homological finiteness. Chapter 6 presents special classes of invariants, which deal with modular invariant theory and its particular problems and features. Chapter 7 collects results for special classes of invariants and coinvariants such as (pseudo) reflection groups and representations of low degree. If the ground field is finite, additional problems appear and are compensated for in part by the emergence of new tools. One of these is the Steenrod algebra, which the authors introduce in Chapter 8 to solve the inverse invariant theory problem, around which the authors have organized the last three chapters. The book contains numerous examples to illustrate the theory, often of more than passing interest, and an appendix on commutative graded algebra, which provides some of the required basic background. There is an extensive reference list to provide the reader with orientation to the vast literature.


Book Synopsis Invariant Theory of Finite Groups by : Mara D. Neusel

Download or read book Invariant Theory of Finite Groups written by Mara D. Neusel and published by American Mathematical Soc.. This book was released on 2010-03-08 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The questions that have been at the center of invariant theory since the 19th century have revolved around the following themes: finiteness, computation, and special classes of invariants. This book begins with a survey of many concrete examples chosen from these themes in the algebraic, homological, and combinatorial context. In further chapters, the authors pick one or the other of these questions as a departure point and present the known answers, open problems, and methods and tools needed to obtain these answers. Chapter 2 deals with algebraic finiteness. Chapter 3 deals with combinatorial finiteness. Chapter 4 presents Noetherian finiteness. Chapter 5 addresses homological finiteness. Chapter 6 presents special classes of invariants, which deal with modular invariant theory and its particular problems and features. Chapter 7 collects results for special classes of invariants and coinvariants such as (pseudo) reflection groups and representations of low degree. If the ground field is finite, additional problems appear and are compensated for in part by the emergence of new tools. One of these is the Steenrod algebra, which the authors introduce in Chapter 8 to solve the inverse invariant theory problem, around which the authors have organized the last three chapters. The book contains numerous examples to illustrate the theory, often of more than passing interest, and an appendix on commutative graded algebra, which provides some of the required basic background. There is an extensive reference list to provide the reader with orientation to the vast literature.

Invariant Theory

Invariant Theory

Author: John Fogarty

Publisher:

Published: 1969

Total Pages: 240

ISBN-13:

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Book Synopsis Invariant Theory by : John Fogarty

Download or read book Invariant Theory written by John Fogarty and published by . This book was released on 1969 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Invariant Theory in All Characteristics

Invariant Theory in All Characteristics

Author: Harold Edward Alexander Eddy Campbell

Publisher: American Mathematical Soc.

Published:

Total Pages: 308

ISBN-13: 9780821870303

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This volume includes the proceedings of a workshop on Invariant Theory held at Queen's University (Ontario). The workshop was part of the theme year held under the auspices of the Centre de recherches mathematiques (CRM) in Montreal. The gathering brought together two communities of researchers: those working in characteristic 0 and those working in positive characteristic. The book contains three types of papers: survey articles providing introductions to computational invarianttheory, modular invariant theory of finite groups, and the invariant theory of Lie groups; expository works recounting recent research in these three areas and beyond; and open problems of current interest. The book is suitable for graduate students and researchers working in invarianttheory.


Book Synopsis Invariant Theory in All Characteristics by : Harold Edward Alexander Eddy Campbell

Download or read book Invariant Theory in All Characteristics written by Harold Edward Alexander Eddy Campbell and published by American Mathematical Soc.. This book was released on with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes the proceedings of a workshop on Invariant Theory held at Queen's University (Ontario). The workshop was part of the theme year held under the auspices of the Centre de recherches mathematiques (CRM) in Montreal. The gathering brought together two communities of researchers: those working in characteristic 0 and those working in positive characteristic. The book contains three types of papers: survey articles providing introductions to computational invarianttheory, modular invariant theory of finite groups, and the invariant theory of Lie groups; expository works recounting recent research in these three areas and beyond; and open problems of current interest. The book is suitable for graduate students and researchers working in invarianttheory.

Representations and Nilpotent Orbits of Lie Algebraic Systems

Representations and Nilpotent Orbits of Lie Algebraic Systems

Author: Maria Gorelik

Publisher: Springer Nature

Published: 2019-10-18

Total Pages: 553

ISBN-13: 3030235319

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This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.


Book Synopsis Representations and Nilpotent Orbits of Lie Algebraic Systems by : Maria Gorelik

Download or read book Representations and Nilpotent Orbits of Lie Algebraic Systems written by Maria Gorelik and published by Springer Nature. This book was released on 2019-10-18 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.