The Resource Introduction to Lie algebras, Karin Erdmann and Mark J. Wildon
Introduction to Lie algebras, Karin Erdmann and Mark J. Wildon
Resource Information
The item Introduction to Lie algebras, Karin Erdmann and Mark J. Wildon represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Introduction to Lie algebras, Karin Erdmann and Mark J. Wildon represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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 fourthyear undergraduates, this book provides an elementary introduction to Lie algebras. It starts with basic concepts. A section on lowdimensional 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 finitedimensional complex Lie algebras. The next chapters cover Engel's theorem, Lie's theorem and Cartan's criteria and introduce some representation theory. The rootspace 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 presentday 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 selfstudy guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics
 Language
 eng
 Extent
 1 online resource (x, 251 pages)
 Contents

 Ideals and Homomorphisms
 LowDimensional 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
 Isbn
 9781846284908
 Label
 Introduction to Lie algebras
 Title
 Introduction to Lie algebras
 Statement of responsibility
 Karin Erdmann and Mark J. Wildon
 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 fourthyear undergraduates, this book provides an elementary introduction to Lie algebras. It starts with basic concepts. A section on lowdimensional 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 finitedimensional complex Lie algebras. The next chapters cover Engel's theorem, Lie's theorem and Cartan's criteria and introduce some representation theory. The rootspace 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 presentday 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 selfstudy guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics
 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
 Bibliography note
 Includes bibliographical references (pages 247248) 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  LowDimensional 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
 10.1007/1846284902
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9781846280405
 Specific material designation
 remote
 System control number
 (OCoLC)209948735
 Label
 Introduction to Lie algebras, Karin Erdmann and Mark J. Wildon
 Bibliography note
 Includes bibliographical references (pages 247248) 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  LowDimensional 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
 10.1007/1846284902
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9781846280405
 Specific material designation
 remote
 System control number
 (OCoLC)209948735
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