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Introduction to representation theory

Introduction to representation theoryPavel Etingof, Oleg Golberg, Sebastian Hensel,Tiankai Liu, Alex Schwendner, Dmitry Vaintrob, and Elena YudovinaJanuary 10, 2011 Contents1 Basic notions of representation What is representation theory ? .. Algebras .. Representations .. Ideals .. Quotients .. Algebras defined by generators and relations .. Examples of algebras .. Quivers .. Lie algebras .. Tensor products .. The tensor algebra .. Hilbert s third problem .. Tensor products and duals of representations of Lie algebras .. Representations ofsl(2) .. Problems on Lie algebras .. 212 General results of representation Subrepresentations in semisimple representations.

them Dynkin diagrams would be the best choice! As a final example consider the representation theory of finite groups, which is one of the most fascinating chapters of representation theory. In this theory, one considers representations of the group algebra A= C[G] of a finite group G– the algebra with basis ag,g∈ Gand multiplication

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