Quiver Representations And Quiver Varieties


Quiver Representations And Quiver Varieties
Author: Alexander Kirillov Jr.
Publisher: American Mathematical Soc.
ISBN: 1470423073
Size: 53.39 MB
Format: PDF
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Quiver Representations And Quiver Varieties

Quiver Representations And Quiver Varieties by Alexander Kirillov Jr., Quiver Representations And Quiver Varieties Books available in PDF, EPUB, Mobi Format. Download Quiver Representations And Quiver Varieties books, 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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Language: en
Pages: 295
Authors: Alexander Kirillov Jr.
Categories: Algebraic geometry -- Cycles and subschemes -- Parametrization (Chow and Hilbert schemes)
Type: BOOK - Published: 2016-08-25 - Publisher: American Mathematical Soc.
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
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Language: en
Pages: 344
Authors: Harm Derksen, Jerzy Weyman
Categories: Directed graphs
Type: BOOK - Published: 2017-11-29 - Publisher: American Mathematical Soc.
This book is an introduction to the representation theory of quivers and finite dimensional algebras. It gives a thorough and modern treatment of the algebraic approach based on Auslander-Reiten theory as well as the approach based on geometric invariant theory. The material in the opening chapters is developed starting slowly
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Language: en
Pages: 371
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Categories: Mathematics
Type: BOOK - Published: 2020-02-20 - Publisher: Springer Nature
This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types. Although the theory of Gröbner bases was
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Pages: 479
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Categories: Mathematics
Type: BOOK - Published: 2004 - Publisher: American Mathematical Soc.
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Language: en
Pages: 213
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Lie theory has connections to many other disciplines such as geometry, number theory, mathematical physics, and algebraic combinatorics. The interaction between algebra, geometry and combinatorics has proven to be extremely powerful in shedding new light on each of these areas. This book presents the lectures given at the Fields Institute
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Language: en
Pages:
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Type: BOOK - Published: 2008-10 - Publisher:
Books about Mathematical Reviews
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Pages: 406
Authors: Raymundo Bautista, Roberto Martínez-Villa, Jos?e Antonio de la Pe?na, Workshop on Representation Theory of Algebras and Related Topics (1994 : Mexico City, Mexico)
Categories: Mathematics
Type: BOOK - Published: 1996 - Publisher: American Mathematical Soc.
These proceedings report a number of lecture series delivered during the Workshop on Representation Theory of Algebras and Related Topics held at Universidad Nacional Autonoma de Mexico (UNAM) in August 1994. The workshop was dedicated to recent advances in the field and its interaction with other areas of mathematics, such
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Language: en
Pages: 223
Authors: Caroline Gruson, Vera Serganova
Categories: Mathematics
Type: BOOK - Published: 2018-10-23 - Publisher: Springer
This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text
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Language: en
Pages: 3500
Authors: Jean-Pierre Françoise, Gregory L. Naber, Tsou Sheung Tsun
Categories: Science
Type: BOOK - Published: 2006-06-20 - Publisher: Academic Press
The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to
Poisson Algebraic Geometry in Representation Theory and Combinatorics
Language: en
Pages: 182
Authors: Benjamin Thomas Webster
Categories: Science
Type: BOOK - Published: 2007 - Publisher:
Books about Poisson Algebraic Geometry in Representation Theory and Combinatorics