Description

Book Synopsis

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.

Table of Contents

Finite-Dimensional Modules; The Universal Enveloping Algebra; Weight Modules; The Primitive Spectrum; Category O; Description of All Simple Modules; Categorification of Finite-Dimensional Modules.

Lectures On Sl_2(c)-modules

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    A Hardback by Volodymyr Mazorchuk

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      Book details

      Publisher Imperial College Press
      Published 11 December 2009
      ISBN-13 9781848165175
      978-1848165175
      ISBN-10 184816517X
      Also in:
      Algebra

      Description

      Book Synopsis

      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.

      Table of Contents

      Finite-Dimensional Modules; The Universal Enveloping Algebra; Weight Modules; The Primitive Spectrum; Category O; Description of All Simple Modules; Categorification of Finite-Dimensional Modules.

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