The Resource Representations of Lie algebras : an introduction through gln, Anthony Henderson, (electronic resource)

Representations of Lie algebras : an introduction through gln, Anthony Henderson, (electronic resource)

Label
Representations of Lie algebras : an introduction through gln
Title
Representations of Lie algebras
Title remainder
an introduction through gln
Statement of responsibility
Anthony Henderson
Creator
Subject
Genre
Language
  • eng
  • eng
Summary
A fresh undergraduate-accessible approach to Lie algebras and their representations
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorDate
1976-
http://library.link/vocab/creatorName
Henderson, Anthony
Dewey number
512.482
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA252.3
LC item number
.H46 2012
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Australian Mathematical Society lecture series
Series volume
22
http://library.link/vocab/subjectName
  • Representations of Lie algebras
  • Lie algebras
Label
Representations of Lie algebras : an introduction through gln, Anthony Henderson, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • 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 algebra4.1 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 irreducibles7.5 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
Dimensions
unknown
Extent
1 online resource (168 p.)
Form of item
online
Isbn
9781139555166
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000234802
  • (EBL)989151
  • (OCoLC)808501344
  • (SSID)ssj0000741775
  • (PQKBManifestationID)11473265
  • (PQKBTitleCode)TC0000741775
  • (PQKBWorkID)10743023
  • (PQKB)10563011
  • (UkCbUP)CR9781139236126
  • (MiAaPQ)EBC989151
  • (EXLCZ)992670000000234802
Label
Representations of Lie algebras : an introduction through gln, Anthony Henderson, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • 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 algebra4.1 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 irreducibles7.5 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
Dimensions
unknown
Extent
1 online resource (168 p.)
Form of item
online
Isbn
9781139555166
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000234802
  • (EBL)989151
  • (OCoLC)808501344
  • (SSID)ssj0000741775
  • (PQKBManifestationID)11473265
  • (PQKBTitleCode)TC0000741775
  • (PQKBWorkID)10743023
  • (PQKB)10563011
  • (UkCbUP)CR9781139236126
  • (MiAaPQ)EBC989151
  • (EXLCZ)992670000000234802

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