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A journey through representation theory = from finite groups to quivers via algebras /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	A journey through representation theory/ by Caroline Gruson, Vera Serganova.
Reminder of title:	from finite groups to quivers via algebras /
Author:	Gruson, Caroline.
other author:	Serganova, Vera.
Published:	Cham :Springer International Publishing : : 2018.,
Description:	xiii, 223 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Representations of groups. -
Online resource:	https://doi.org/10.1007/978-3-319-98271-7
ISBN:	9783319982717

A journey through representation theory = from finite groups to quivers via algebras /
Gruson, Caroline.

A journey through representation theoryfrom finite groups to quivers via algebras /[electronic resource] :by Caroline Gruson, Vera Serganova. - Cham :Springer International Publishing :2018. - xiii, 223 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

Introduction to Representation Theory of Finite Groups -- Modules with Applications to Finite Groups -- Representations of Compact Groups -- Results About Unitary Representations -- On Algebraic Methods -- Symmetric Groups, Schur-Weyl Duality and Positive Self-adjoint Hopf Algebras -- Introduction to representation theory of quivers -- Representations of Dynkin and affine quivers -- Applications of quivers -- Bibliography -- Index.

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 includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2) Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.

ISBN: 9783319982717

Standard No.: 10.1007/978-3-319-98271-7doiSubjects--Topical Terms:

672181
Representations of groups.

LC Class. No.: QA176 / .G787 2018

Dewey Class. No.: 512.22

A journey through representation theory = from finite groups to quivers via algebras /
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245 1 2 $a A journey through representation theory $h [electronic resource] : $b from finite groups to quivers via algebras / $c by Caroline Gruson, Vera Serganova.
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490 1 $a Universitext, $x 0172-5939
505 0 $a Introduction to Representation Theory of Finite Groups -- Modules with Applications to Finite Groups -- Representations of Compact Groups -- Results About Unitary Representations -- On Algebraic Methods -- Symmetric Groups, Schur-Weyl Duality and Positive Self-adjoint Hopf Algebras -- Introduction to representation theory of quivers -- Representations of Dynkin and affine quivers -- Applications of quivers -- Bibliography -- Index.
520 $a 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 includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2) Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.
650 0 $a Representations of groups. $3 672181
650 0 $a Representations of algebras. $3 902229
650 1 4 $a Group Theory and Generalizations. $3 672112
700 1 $a Serganova, Vera. $3 1210582
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856 4 0 $u https://doi.org/10.1007/978-3-319-98271-7
950 $a Mathematics and Statistics (Springer-11649)