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A journey through representation the...

Gruson, Caroline.

A journey through representation theoryfrom finite groups to quivers via algebras /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A journey through representation theoryby Caroline Gruson, Vera Serganova.
其他題名:	from finite groups to quivers via algebras /
作者:	Gruson, Caroline.
其他作者:	Serganova, Vera.
出版者:	Cham :Springer International Publishing :2018.
面頁冊數:	xiii, 223 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Representations of groups.
電子資源:	https://doi.org/10.1007/978-3-319-98271-7
ISBN:	9783319982717$q(electronic bk.)

A journey through representation theoryfrom 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$q(electronic bk.)

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

191076
Representations of groups.

LC Class. No.: QA176 / .G787 2018

Dewey Class. No.: 512.22

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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 191076
650 0 $a Representations of algebras. $3 191077
650 1 4 $a Group Theory and Generalizations. $3 274819
700 1 $a Serganova, Vera. $3 824932
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950 $a Mathematics and Statistics (Springer-11649)