Overview
Systematically presents the structure theory of general, unrestricted Lie groups
Self-contained, with two appendices on covering theory and multilinear algebra
Includes abundant classroom-tested exercises
Useful as both a graduate text and as a research reference for a broad range of mathematicians
Includes supplementary material: sn.pub/extras
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (18 chapters)
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Front Matter
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Matrix Groups
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Front Matter
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Lie Algebras
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Front Matter
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Manifolds and Lie Groups
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Front Matter
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Structure Theory of Lie Groups
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Front Matter
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Keywords
About this book
This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity.
This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference.
Reviews
From the reviews:
“The monograph under review is an introduction to the structure theory and geometry of Lie groups accessible both to a broad range of mathematicians and to graduate students. … The book consists of twenty one chapters divided into five parts. It starts with an introduction which presents the structure of the book, contains various teaching suggestions and introduces some fundamental notation.” (Volodymyr Mazorchuk, Zentralblatt MATH, Vol. 1229, 2012)
Authors and Affiliations
Bibliographic Information
Book Title: Structure and Geometry of Lie Groups
Authors: Joachim Hilgert, Karl-Hermann Neeb
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-0-387-84794-8
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2012
Hardcover ISBN: 978-0-387-84793-1Published: 05 November 2011
Softcover ISBN: 978-1-4899-9006-8Published: 25 January 2014
eBook ISBN: 978-0-387-84794-8Published: 06 November 2011
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: X, 746
Topics: Topological Groups, Lie Groups, Differential Geometry, Algebraic Topology, Algebra