Quiver Representations

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Quiver Representations

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Author : Ralf Schiffler
language : en
Publisher: Springer
Release Date : 2014-09-04

Quiver Representations written by Ralf Schiffler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-04 with Mathematics categories.

This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel’s Theorem. The language of category theory is developed along the way as needed.

Quiver Representations And Quiver Varieties

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Author : Alexander Kirillov Jr.
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-08-25

Quiver Representations And Quiver Varieties written by Alexander Kirillov Jr. and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-25 with Mathematics categories.

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.

An Introduction To Quiver Representations

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Author : Harm Derksen
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-11-29

An Introduction To Quiver Representations written by Harm Derksen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-29 with Mathematics categories.

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 with topics such as homological algebra, Morita equivalence, and Gabriel's theorem. Next, the book presents Auslander-Reiten theory, including almost split sequences and the Auslander-Reiten transform, and gives a proof of Kac's generalization of Gabriel's theorem. Once this basic material is established, the book goes on with developing the geometric invariant theory of quiver representations. The book features the exposition of the saturation theorem for semi-invariants of quiver representations and its application to Littlewood-Richardson coefficients. In the final chapters, the book exposes tilting modules, exceptional sequences and a connection to cluster categories. The book is suitable for a graduate course in quiver representations and has numerous exercises and examples throughout the text. The book will also be of use to experts in such areas as representation theory, invariant theory and algebraic geometry, who want to learn about applications of quiver representations to their fields.

Representation Theory Of Algebraic Groups And Quantum Groups

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Author : Toshiaki Shoji
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2004

Representation Theory Of Algebraic Groups And Quantum Groups written by Toshiaki Shoji and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.

A collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference. This title presents an overview of developments in representation theory of algebraic groups and quantum groups. It includes papers containing results concerning Lusztig's conjecture on cells in affine Weyl groups.

Representations Of Algebras

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Author : V. Dlab
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1975-09

Representations Of Algebras written by V. Dlab and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-09 with Mathematics categories.

Quiver Representations And Their Dense Orbits

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Author : Danny Lara
language : en
Publisher:
Release Date : 2019

Quiver Representations And Their Dense Orbits written by Danny Lara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Directed graphs categories.

We can view quiver representations of a fixed dimension vector as an algebraic variety over an algebraically closed field $K$. There is an action of the product of general linear groups on each of these varieties where the orbits of the action correspond to isomorphism classes of quiver representation. A $K$-algebra $A$ is said to have the dense orbit property if for each dimension vector, the product of the general linear group acts on each irreducible component of the module variety with a dense orbit. Under certain conditions, a $K$ algebra $A$ is representation finite if and only if it $A$ has the dense orbit property. The implication representation finite implies the dense orbit property is always true. The converse is not true in general, as shown by Chindris, Kinser, and Weyman in \cite{ryan}. Our main theorem of this thesis builds on their work to give a family of representation infinite algebras with the dense orbit property. We also give a conjectured classification of indecomposables with dense orbits. \par In the future, we hope the work presented here can be used to find even more examples of representation infinite algebra with the dense orbit property to then develop deeper theory to classify algebras with the dense orbit property that are representation infinite.

Computational Methods For Representations Of Groups And Algebras

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Author : P. Dräxler
language : en
Publisher: Birkhauser
Release Date : 1999

Computational Methods For Representations Of Groups And Algebras written by P. Dräxler and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

Mathematics Of The Ussr

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Author :
language : en
Publisher:
Release Date : 1992

Mathematics Of The Ussr written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

Representations Of Cartan Type Lie Superalgebras

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Author : Noam Shomron
language : en
Publisher:
Release Date : 2001

Representations Of Cartan Type Lie Superalgebras written by Noam Shomron and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2008

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.