Coverart for item
The Resource Introduction to Lie algebras, Karin Erdmann and Mark J. Wildon

Introduction to Lie algebras, Karin Erdmann and Mark J. Wildon

Label
Introduction to Lie algebras
Title
Introduction to Lie algebras
Statement of responsibility
Karin Erdmann and Mark J. Wildon
Creator
Contributor
Subject
Language
eng
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. Based on a lecture course given to fourth-year undergraduates, this book provides an elementary introduction to Lie algebras. It starts with basic concepts. A section on low-dimensional Lie algebras provides readers with experience of some useful examples. This is followed by a discussion of solvable Lie algebras and a strategy towards a classification of finite-dimensional complex Lie algebras. The next chapters cover Engel's theorem, Lie's theorem and Cartan's criteria and introduce some representation theory. The root-space decomposition of a semisimple Lie algebra is discussed, and the classical Lie algebras studied in detail. The authors also classify root systems, and give an outline of Serre's construction of complex semisimple Lie algebras. An overview of further directions then concludes the book and shows the high degree to which Lie algebras influence present-day mathematics. 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 worked 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
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1948-
http://library.link/vocab/creatorName
Erdmann, Karin
Dewey number
512.482
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA252.3
LC item number
.E73 2006eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Wildon, Mark J
Series statement
Springer undergraduate mathematics series,
http://library.link/vocab/subjectName
  • Lie algebras
  • Lie algebras
  • Lie algebras
Label
Introduction to Lie algebras, Karin Erdmann and Mark J. Wildon
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 247-248) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Ideals and Homomorphisms -- Low-Dimensional Lie Algebras -- Solvable Lie Algebras and a Rough Classification -- Subalgebras of gl(V) -- Engel's Theorem and Lie's Theorem -- Some Representation Theory -- Representations of sl(2, C) -- Cartan's Criteria -- The Root Space Decomposition -- Root Systems -- The Classical Lie Algebras -- The Classification of Root Systems -- Simple Lie Algebras -- Further Directions -- Appendix A: Linear Algebra -- Appendix B: Weyl's Theorem -- Appendix C: Cartan Subalgebras -- Appendix D: Weyl Groups -- Appendix E: Answers to Selected Exercises
Control code
209948735
Dimensions
unknown
Extent
1 online resource (x, 251 pages)
Form of item
online
Isbn
9781846284908
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/1-84628-490-2
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-1-84628-040-5
Specific material designation
remote
System control number
(OCoLC)209948735
Label
Introduction to Lie algebras, Karin Erdmann and Mark J. Wildon
Publication
Bibliography note
Includes bibliographical references (pages 247-248) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Ideals and Homomorphisms -- Low-Dimensional Lie Algebras -- Solvable Lie Algebras and a Rough Classification -- Subalgebras of gl(V) -- Engel's Theorem and Lie's Theorem -- Some Representation Theory -- Representations of sl(2, C) -- Cartan's Criteria -- The Root Space Decomposition -- Root Systems -- The Classical Lie Algebras -- The Classification of Root Systems -- Simple Lie Algebras -- Further Directions -- Appendix A: Linear Algebra -- Appendix B: Weyl's Theorem -- Appendix C: Cartan Subalgebras -- Appendix D: Weyl Groups -- Appendix E: Answers to Selected Exercises
Control code
209948735
Dimensions
unknown
Extent
1 online resource (x, 251 pages)
Form of item
online
Isbn
9781846284908
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/1-84628-490-2
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-1-84628-040-5
Specific material designation
remote
System control number
(OCoLC)209948735

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