Lectures on sl2 (C)-modules

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. Preface Contents Chapter 1 Finite-dimensional modules Chapter 2 The universal enveloping algebra Chapter 3 Weight modules Chapter 4 The primitive spectrum Chapter 5 Category O Chapter 6 Description of all simple modules Chapter 7 Categorification of simple finite-dimensional modules Appendix A Answers and hints to exercises Bibliography Index of Notation Index Directed primarily at undergraduate and postgraduate students interested to get acquainted with the representation theory of Lie algebras, this book treats the case of the smallest simple Lie algebra, namely, the Lie algebra sl_2. It also contains an account of a new research direction: the categorification of simple finite-dimensional modules.