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Frobenius Algebras and 2-D Topological Quantum Field Theories

Author: Joachim Kock

Publisher: Cambridge University Press

Published: 2004

Total Pages: 260

ISBN-13: 9780521540315

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This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work.

Book Synopsis Frobenius Algebras and 2-D Topological Quantum Field Theories by : Joachim Kock

Download or read book Frobenius Algebras and 2-D Topological Quantum Field Theories written by Joachim Kock and published by Cambridge University Press. This book was released on 2004 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work.

Frobenius Algebras

Author: Andrzej Skowroński

Publisher: European Mathematical Society

Published: 2011

Total Pages: 672

ISBN-13: 9783037191026

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This is the first of two volumes which will provide a comprehensive introduction to the modern representation theory of Frobenius algebras. The first part of the book serves as a general introduction to basic results and techniques of the modern representation theory of finite dimensional associative algebras over fields, including the Morita theory of equivalences and dualities and the Auslander-Reiten theory of irreducible morphisms and almost split sequences. The second part is devoted to fundamental classical and recent results concerning the Frobenius algebras and their module categories. Moreover, the prominent classes of Frobenius algebras, the Hecke algebras of Coxeter groups, and the finite dimensional Hopf algebras over fields are exhibited. This volume is self contained and the only prerequisite is a basic knowledge of linear algebra. It includes complete proofs of all results presented and provides a rich supply of examples and exercises. The text is primarily addressed to graduate students starting research in the representation theory of algebras as well as mathematicians working in other fields.

Book Synopsis Frobenius Algebras by : Andrzej Skowroński

Download or read book Frobenius Algebras written by Andrzej Skowroński and published by European Mathematical Society. This book was released on 2011 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of two volumes which will provide a comprehensive introduction to the modern representation theory of Frobenius algebras. The first part of the book serves as a general introduction to basic results and techniques of the modern representation theory of finite dimensional associative algebras over fields, including the Morita theory of equivalences and dualities and the Auslander-Reiten theory of irreducible morphisms and almost split sequences. The second part is devoted to fundamental classical and recent results concerning the Frobenius algebras and their module categories. Moreover, the prominent classes of Frobenius algebras, the Hecke algebras of Coxeter groups, and the finite dimensional Hopf algebras over fields are exhibited. This volume is self contained and the only prerequisite is a basic knowledge of linear algebra. It includes complete proofs of all results presented and provides a rich supply of examples and exercises. The text is primarily addressed to graduate students starting research in the representation theory of algebras as well as mathematicians working in other fields.

New Examples of Frobenius Extensions

Author: Lars Kadison

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 98

ISBN-13: 0821819623

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This volume is based on the author's lecture courses to algebraists at Munich and at Goteborg. He presents a unified approach from the point of view of Frobenius algebras/extensions. The book is intended for graduate students and research mathematicians working in algebra and topology.

Book Synopsis New Examples of Frobenius Extensions by : Lars Kadison

Download or read book New Examples of Frobenius Extensions written by Lars Kadison and published by American Mathematical Soc.. This book was released on 1999 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the author's lecture courses to algebraists at Munich and at Goteborg. He presents a unified approach from the point of view of Frobenius algebras/extensions. The book is intended for graduate students and research mathematicians working in algebra and topology.

Encyclopedic Dictionary of Mathematics

Author: Nihon Sūgakkai

Publisher: MIT Press

Published: 1993

Total Pages: 1180

ISBN-13: 9780262590204

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V.1. A.N. v.2. O.Z. Apendices and indexes.

Book Synopsis Encyclopedic Dictionary of Mathematics by : Nihon Sūgakkai

Download or read book Encyclopedic Dictionary of Mathematics written by Nihon Sūgakkai and published by MIT Press. This book was released on 1993 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A.N. v.2. O.Z. Apendices and indexes.

Galois Theory, Hopf Algebras, and Semiabelian Categories

Author: George Janelidze, Bodo Pareigis, and Walter Tholen

Publisher: American Mathematical Soc.

Published:

Total Pages: 588

ISBN-13: 9780821871478

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Book Synopsis Galois Theory, Hopf Algebras, and Semiabelian Categories by : George Janelidze, Bodo Pareigis, and Walter Tholen

Download or read book Galois Theory, Hopf Algebras, and Semiabelian Categories written by George Janelidze, Bodo Pareigis, and Walter Tholen and published by American Mathematical Soc.. This book was released on with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebras, Rings and Modules

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

Published: 2007

Total Pages: 405

ISBN-13: 1402051409

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Book Synopsis Algebras, Rings and Modules by : Michiel Hazewinkel

Download or read book Algebras, Rings and Modules written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2007 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometry, Topology, and Mathematical Physics

Author: V. M. Buchstaber

Publisher: American Mathematical Soc.

Published: 2008-01-01

Total Pages: 304

ISBN-13: 9780821890769

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This volume contains a selection of papers based on presentations given in 2006-2007 at the S. P. Novikov Seminar at the Steklov Mathematical Institute in Moscow. Novikov's diverse interests are reflected in the topics presented in the book. The articles address topics in geometry, topology, and mathematical physics. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.

Book Synopsis Geometry, Topology, and Mathematical Physics by : V. M. Buchstaber

Download or read book Geometry, Topology, and Mathematical Physics written by V. M. Buchstaber and published by American Mathematical Soc.. This book was released on 2008-01-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of papers based on presentations given in 2006-2007 at the S. P. Novikov Seminar at the Steklov Mathematical Institute in Moscow. Novikov's diverse interests are reflected in the topics presented in the book. The articles address topics in geometry, topology, and mathematical physics. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.

Associative and Non-Associative Algebras and Applications

Author: Mercedes Siles Molina

Publisher: Springer Nature

Published: 2020-01-02

Total Pages: 338

ISBN-13: 3030352560

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This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April 12-14, 2018, and which reflects the mathematical collaboration between south European and north African countries, mainly France, Spain, Morocco, Tunisia and Senegal. The book is divided in three parts and features contributions from the following fields: algebraic and analytic methods in associative and non-associative structures; homological and categorical methods in algebra; and history of mathematics. Covering topics such as rings and algebras, representation theory, number theory, operator algebras, category theory, group theory and information theory, it opens up new avenues of study for graduate students and young researchers. The findings presented also appeal to anyone interested in the fields of algebra and mathematical analysis.

Book Synopsis Associative and Non-Associative Algebras and Applications by : Mercedes Siles Molina

Download or read book Associative and Non-Associative Algebras and Applications written by Mercedes Siles Molina and published by Springer Nature. This book was released on 2020-01-02 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April 12-14, 2018, and which reflects the mathematical collaboration between south European and north African countries, mainly France, Spain, Morocco, Tunisia and Senegal. The book is divided in three parts and features contributions from the following fields: algebraic and analytic methods in associative and non-associative structures; homological and categorical methods in algebra; and history of mathematics. Covering topics such as rings and algebras, representation theory, number theory, operator algebras, category theory, group theory and information theory, it opens up new avenues of study for graduate students and young researchers. The findings presented also appeal to anyone interested in the fields of algebra and mathematical analysis.

Semigroups Having Quasi-frobenius Algebras

Author: Ronald Harold Wenger

Publisher:

Published: 1965

Total Pages: 152

ISBN-13:

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Book Synopsis Semigroups Having Quasi-frobenius Algebras by : Ronald Harold Wenger

Download or read book Semigroups Having Quasi-frobenius Algebras written by Ronald Harold Wenger and published by . This book was released on 1965 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Finite-Dimensional Division Algebras Over Fields

Author: Nathan Jacobson

Publisher: Springer Science & Business Media

Published: 1996

Total Pages: 290

ISBN-13: 3540570292

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Finite-dimensional division algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensio= nal algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brau= er-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts;they arose first in the study of the so-called "multiplication algebras of Riemann matrices". The largest part of the book is the fifth chapter, dealing with involu= torial simple algebras of finite dimension over a field. Of particular interest are the Jordan algebras determined by these algebras with involution;their structure is discussed. Two important concepts of these algebras with involution are the universal enveloping algebras and the reduced norm. Corrections of the 1st edition (1996) carried out on behalf of N. Jacobson (deceased) by Prof. P.M. Cohn (UC London, UK).

Book Synopsis Finite-Dimensional Division Algebras Over Fields by : Nathan Jacobson

Download or read book Finite-Dimensional Division Algebras Over Fields written by Nathan Jacobson and published by Springer Science & Business Media. This book was released on 1996 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite-dimensional division algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensio= nal algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brau= er-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts;they arose first in the study of the so-called "multiplication algebras of Riemann matrices". The largest part of the book is the fifth chapter, dealing with involu= torial simple algebras of finite dimension over a field. Of particular interest are the Jordan algebras determined by these algebras with involution;their structure is discussed. Two important concepts of these algebras with involution are the universal enveloping algebras and the reduced norm. Corrections of the 1st edition (1996) carried out on behalf of N. Jacobson (deceased) by Prof. P.M. Cohn (UC London, UK).