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A Journey Through Representation Theory: From Finite Groups to Quivers via Algebras

✍ Scribed by Caroline Gruson, Vera Serganova

Publisher
Springer International Publishing
Year
2018
Tongue
English
Leaves
231
Series
Universitext
Edition
1st ed.
Category
Library
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✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xiii
Introduction to representation theory of finite groups (Caroline Gruson, Vera Serganova)....Pages 1-23
Modules with applications to finite groups (Caroline Gruson, Vera Serganova)....Pages 25-46
Representations of compact groups (Caroline Gruson, Vera Serganova)....Pages 47-63
Results about unitary representations (Caroline Gruson, Vera Serganova)....Pages 65-80
On algebraic methods (Caroline Gruson, Vera Serganova)....Pages 81-104
Symmetric groups, Schur–Weyl duality and positive self-adjoint Hopf algebras (Caroline Gruson, Vera Serganova)....Pages 105-147
Introduction to representation theory of quivers (Caroline Gruson, Vera Serganova)....Pages 149-168
Representations of Dynkin and affine quivers (Caroline Gruson, Vera Serganova)....Pages 169-191
Applications of quivers (Caroline Gruson, Vera Serganova)....Pages 193-217
Back Matter ....Pages 219-223

✦ Subjects

Mathematics; Group Theory and Generalizations

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