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Introduction to lie algebras / Karin Erdmann and Mark J. Wildon.

By: Contributor(s): Material type: TextTextSeries: Springer undergraduate mathematics seriesPublication details: London : Springer, c2006.Description: x, 251 p. : ill. ; 24 cmISBN:
  • 9781846280405 (pbk.)
  • 9781846284908 (ebook)
Other title:
  • Introduction to lie algebras [electronic resource]
Subject(s): DDC classification:
  • 512 ERD
LOC classification:
  • QA252.3 .E73 2006
Also available in online version.
Contents:
Introduction Karin Erdmann, Mark J. Wildon Pages 1-9 Ideals and Homomorphisms Karin Erdmann, Mark J. Wildon Pages 11-17 Low-Dimensional Lie Algebras Karin Erdmann, Mark J. Wildon Pages 19-26 Solvable Lie Algebras and a Rough Classification Karin Erdmann, Mark J. Wildon Pages 27-36 Subalgebras of gl(V) Karin Erdmann, Mark J. Wildon Pages 37-44 Engel’s Theorem and Lie’s Theorem Karin Erdmann, Mark J. Wildon Pages 45-52 Some Representation Theory Karin Erdmann, Mark J. Wildon Pages 53-65 Representations of sl(2, C) Karin Erdmann, Mark J. Wildon Pages 67-76 Cartan’s Criteria Karin Erdmann, Mark J. Wildon Pages 77-90 The Root Space Decomposition Karin Erdmann, Mark J. Wildon Pages 91-107 Root Systems Karin Erdmann, Mark J. Wildon Pages 109-124 The Classical Lie Algebras Karin Erdmann, Mark J. Wildon Pages 125-139 The Classification of Root Systems Karin Erdmann, Mark J. Wildon Pages 141-152 Simple Lie Algebras Karin Erdmann, Mark J. Wildon Pages 153-161 Further Directions Karin Erdmann, Mark J. Wildon Pages 163-188 Appendix A: Linear Algebra Karin Erdmann, Mark J. Wildon Pages 189-208 Appendix B: Weyl’s Theorem Karin Erdmann, Mark J. Wildon Pages 209-214 Appendix C: Cartan Subalgebras Karin Erdmann, Mark J. Wildon Pages 215-221 Appendix D: Weyl Groups Karin Erdmann, Mark J. Wildon Pages 223-229 Appendix E: Answers to Selected Exercises Karin Erdmann, Mark J. Wildon Pages 231-246
Summary: Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous work examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.
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Holdings
Item type Current library Collection Call number Status Date due Barcode
Project book Project book CUTN Central Library Sciences Non-fiction 512 ERD (Browse shelf(Opens below)) Checked out to Renuka Devi V (20019T) 31/01/2024 48839

Includes bibliographical references (p. [247]-248) and index.

Introduction
Karin Erdmann, Mark J. Wildon
Pages 1-9
Ideals and Homomorphisms
Karin Erdmann, Mark J. Wildon
Pages 11-17
Low-Dimensional Lie Algebras
Karin Erdmann, Mark J. Wildon
Pages 19-26
Solvable Lie Algebras and a Rough Classification
Karin Erdmann, Mark J. Wildon
Pages 27-36
Subalgebras of gl(V)
Karin Erdmann, Mark J. Wildon
Pages 37-44
Engel’s Theorem and Lie’s Theorem
Karin Erdmann, Mark J. Wildon
Pages 45-52
Some Representation Theory
Karin Erdmann, Mark J. Wildon
Pages 53-65
Representations of sl(2, C)
Karin Erdmann, Mark J. Wildon
Pages 67-76
Cartan’s Criteria
Karin Erdmann, Mark J. Wildon
Pages 77-90
The Root Space Decomposition
Karin Erdmann, Mark J. Wildon
Pages 91-107
Root Systems
Karin Erdmann, Mark J. Wildon
Pages 109-124
The Classical Lie Algebras
Karin Erdmann, Mark J. Wildon
Pages 125-139
The Classification of Root Systems
Karin Erdmann, Mark J. Wildon
Pages 141-152
Simple Lie Algebras
Karin Erdmann, Mark J. Wildon
Pages 153-161
Further Directions
Karin Erdmann, Mark J. Wildon
Pages 163-188
Appendix A: Linear Algebra
Karin Erdmann, Mark J. Wildon
Pages 189-208
Appendix B: Weyl’s Theorem
Karin Erdmann, Mark J. Wildon
Pages 209-214
Appendix C: Cartan Subalgebras
Karin Erdmann, Mark J. Wildon
Pages 215-221
Appendix D: Weyl Groups
Karin Erdmann, Mark J. Wildon
Pages 223-229
Appendix E: Answers to Selected Exercises
Karin Erdmann, Mark J. Wildon
Pages 231-246

Online version restricted to NUS staff and students only through NUSNET.

Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right.

This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous work examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.

Also available in online version.

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