LECTURES ON SL2(C)-MODULES

by Volodymyr Mazorchuk (Uppsala University, Sweden)

Table of Contents (111k)
Preface (80k)
Chapter 1: Finite-dimensional modules (353k)

This book is directed primarily at undergraduate and postgraduate students interested to get acquainted with the representation theory of Lie algebras. The book treats the case of the smallest simple Lie algebra, namely, the Lie algebra sl_2. It contains classical contents including the description of all finite-dimensional modules and an introduction to the universal enveloping algebras with its primitive ideals, alongside non-classical contents including the description of all simple weight modules, the category of all weight modules, a detailed description of the category O, and especially, a description of all simple modules. The book also contains an account of a new research direction: the categorification of simple finite-dimensional modules.
Contents:
  • Finite-Dimensional Modules
  • The Universal Enveloping Algebra
  • Weight Modules
  • The Primitive Spectrum
  • Category O
  • Description of All Simple Modules
  • Categorification of Simple Finite-Dimensional Modules
Readership: Researchers, graduate, undergraduate students and professionals in algebra.
“The book under review is intended to be a textbook for an introductory course on representation theory for advanced undergraduate students or first-year graduate students. It will also be a very useful reference for researchers in any of the numerous branches of modern mathematics and theoretical physics that require some knowledge of Lie algebras and their representations.”
Mathematical Reviews
276pp    Pub. date: Dec 2009  
ISBN:   978-1-84816-517-5
1-84816-517-X 		   US$82 / £54

 

 
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