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Abstract Lie Algebras

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Abstract Lie Algebras Cover

 

Synopses & Reviews

Publisher Comments:

Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. Author David J. Winter, a Professor of Mathematics at the University of Michigan, also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields.

Preliminary material covers modules and nonassociate algebras, followed by a compact, self-contained development of the theory of Lie algebras of characteristic 0. Topics include solvable and nilpotent Lie algebras, Cartan subalgebras, and Levi's radical splitting theorem and the complete reducibility of representations of semisimple Lie algebras. Additional subjects include the isomorphism theorem for semisimple Lie algebras and their irreducible modules, automorphism of Lie algebras, and the conjugacy of Cartan subalgebras and Borel subalgebras. An extensive theory of Cartan and related subalgebras of Lie algebras over arbitrary fields is developed in the final chapter, and an appendix offers background on the Zariski topology.

Synopsis:

Solid but concise, this account emphasizes Lie algebra's simplicity of theory, offering new approaches to major theorems and extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. 1972 edition. 

Synopsis:

Solid but concise, this account emphasizes Lie algebra's simplicity of theory, offering new approaches to major theorems and extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. 1972 edition. 

Table of Contents

Preface
1. Modules
2. Nonassociative Algebras
3. Lie Algebras of Characteristic 0
4. Lie Algebras of Arbitrary Characteristic
Appendix: The Zariski Topology
References
Index

Product Details

ISBN:
9780486462820
Author:
Winter, David
Publisher:
Dover Publications
Author:
Winter, David J.
Author:
Mathematics
Subject:
Algebra - Linear
Subject:
Algebra - Abstract
Subject:
Lie algebras
Subject:
Mathematics-Linear Algebra
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20080131
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
160
Dimensions:
8.5 x 5.38 in 0.38 lb

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Related Subjects

Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Algebra » Lie Groups and Algebra
Science and Mathematics » Mathematics » Algebra » Linear Algebra
Science and Mathematics » Mathematics » Applied
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Abstract Lie Algebras Used Trade Paper
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Product details 160 pages Dover Publications - English 9780486462820 Reviews:
"Synopsis" by ,
Solid but concise, this account emphasizes Lie algebra's simplicity of theory, offering new approaches to major theorems and extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. 1972 edition. 
"Synopsis" by ,
Solid but concise, this account emphasizes Lie algebra's simplicity of theory, offering new approaches to major theorems and extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. 1972 edition. 
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