Record:   Prev Next
Author Henderson, Anthony
Title Representations of Lie Algebras : An Introduction Through gln
Imprint Cambridge : Cambridge University Press, 2012
©2012
book jacket
Descript 1 online resource (168 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Australian Mathematical Society Lecture Series ; v.22
Australian Mathematical Society Lecture Series
Note Cover -- Representations of Lie Algebras -- AUSTRALIAN MATHEMATICAL SOCIETY LECTURE SERIES -- Title -- Copyright -- Contents -- Preface -- Notational conventions -- CHAPTER 1 Motivation: representations of Lie groups -- 1.1 Homomorphisms of general linear groups -- 1.2 Multilinear algebra -- 1.3 Linearization of the problem -- 1.4 Lie's theorem -- CHAPTER 2 Definition of a Lie algebra -- 2.1 Definition and first examples -- 2.2 Classification and isomorphisms -- 2.3 Exercises -- CHAPTER 3 Basic structure of a Lie algebra -- 3.1 Lie subalgebras -- 3.2 Ideals -- 3.3 Quotients and simple Lie algebras -- 3.4 Exercises -- CHAPTER 4 Modules over a Lie algebra -- 4.1 Definition of a module -- 4.2 Isomorphism of modules -- 4.3 Submodules and irreducible modules -- 4.4 Complete reducibility -- 4.5 Exercises -- CHAPTER 5 The theory of sl2-modules -- 5.1 Classification of irreducibles -- 5.2 Complete reducibility -- 5.3 Exercises -- CHAPTER 6 General theory of modules -- 6.1 Duals and tensor products -- 6.2 Hom-spaces and bilinear forms -- 6.3 Schur's lemma and the Killing form -- 6.4 Casimir operators -- 6.5 Exercises -- CHAPTER 7 Integral gln-modules -- 7.1 Integral weights -- 7.2 Highest-weight modules -- 7.3 Irreducibility of highest-weight modules -- 7.4 Tensor-product construction of irreducibles -- 7.5 Complete reducibility -- 7.6 Exercises -- CHAPTER 8 Guide to further reading -- 8.1 Classification of simple Lie algebras -- 8.2 Representations of simple Lie algebras -- 8.3 Characters and bases of representations -- APPENDIX Solutions to the exercises -- Solutions for Chapter 2 exercises -- Solutions for Chapter 3 exercises -- Solutions for Chapter 4 exercises -- Solutions for Chapter 5 exercises -- Solutions for Chapter 6 exercises -- Solutions for Chapter 7 exercises -- References -- Index
A fresh undergraduate-accessible approach to Lie algebras and their representations
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Henderson, Anthony Representations of Lie Algebras : An Introduction Through gln Cambridge : Cambridge University Press,c2012 9781107653610
Subject Representations of Lie algebras.;Lie algebras
Electronic books
Record:   Prev Next