Alexander A. Kirillov's Books

Lectures on Tensor Categories and Modular Functors

By: Bojko Bakalov,Alexander A. Kirillov

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Lectures on Tensor Categories and Modular Functors

By: Bojko Bakalov,Alexander A. Kirillov

This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and Moore-Seiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill. The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advanced-graduate level.

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Page Count

232

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821826867

ISBN 13

9780821826867

Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations

By: Pavel I. Etingof,Igor Frenkel,Alexander A. Kirillov

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Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations

By: Pavel I. Etingof,Igor Frenkel,Alexander A. Kirillov

This text is devoted to mathematical structures arising in conformal field theory and the q-deformations. The authors give a self-contained exposition of the theory of Knizhnik-Zamolodchikov equations and related topics. No previous knowledge of physics is required. The text is suitable for a one-semester graduate course and is intended for graduate students and research mathematicians interested in mathematical physics.

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Page Count

215

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821804960

ISBN 13

9780821804964

An Introduction to Lie Groups and Lie Algebras

By: Alexander A. Kirillov

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An Introduction to Lie Groups and Lie Algebras

By: Alexander A. Kirillov

This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.

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Page Count

237

Publisher

Cambridge University Press

Published Date

ISBN 10

0521889693

ISBN 13

9780521889698

Quiver Representations and Quiver Varieties

By: Alexander Kirillov Jr.

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Quiver Representations and Quiver Varieties

By: Alexander Kirillov Jr.

This book is an introduction to the theory of quiver representations and quiver varieties, starting with basic definitions and ending with Nakajima's work on quiver varieties and the geometric realization of Kac–Moody Lie algebras. The first part of the book is devoted to the classical theory of quivers of finite type. Here the exposition is mostly self-contained and all important proofs are presented in detail. The second part contains the more recent topics of quiver theory that are related to quivers of infinite type: Coxeter functor, tame and wild quivers, McKay correspondence, and representations of Euclidean quivers. In the third part, topics related to geometric aspects of quiver theory are discussed, such as quiver varieties, Hilbert schemes, and the geometric realization of Kac–Moody algebras. Here some of the more technical proofs are omitted; instead only the statements and some ideas of the proofs are given, and the reader is referred to original papers for details. The exposition in the book requires only a basic knowledge of algebraic geometry, differential geometry, and the theory of Lie groups and Lie algebras. Some sections use the language of derived categories; however, the use of this language is reduced to a minimum. The many examples make the book accessible to graduate students who want to learn about quivers, their representations, and their relations to algebraic geometry and Lie algebras.

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Page Count

311

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470423073

ISBN 13

9781470423070

Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory

Villa de Leyva, Colombia, 9-27 July 2001

By: Hernan Ocampo,Sylvie Paycha,Alexander Cardona

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Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory

Villa de Leyva, Colombia, 9-27 July 2001

By: Hernan Ocampo,Sylvie Paycha,Alexander Cardona

This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school.

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Page Count

495

Publisher

World Scientific

Published Date

ISBN 10

9812381317

ISBN 13

9789812381316

Book's by Alexander A. Kirillov

Lectures on Tensor Categories and Modular Functors

Lectures on Tensor Categories and Modular Functors

Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations

Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations

An Introduction to Lie Groups and Lie Algebras

An Introduction to Lie Groups and Lie Algebras

Quiver Representations and Quiver Varieties

Quiver Representations and Quiver Varieties

Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory

Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory

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