Springer Monographs in Mathematics

Structure and Geometry of Lie Groups

Authors: Hilgert, Joachim, Neeb, Karl-Hermann

  • 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
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eBook $139.00
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  • ISBN 978-0-387-84794-8
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  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-0-387-84793-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-1-4899-9006-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
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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)


Table of contents (18 chapters)

  • Introduction

    Hilgert, Joachim (et al.)

    Pages 1-6

  • Concrete Matrix Groups

    Hilgert, Joachim (et al.)

    Pages 9-37

  • The Matrix Exponential Function

    Hilgert, Joachim (et al.)

    Pages 39-60

  • Linear Lie Groups

    Hilgert, Joachim (et al.)

    Pages 61-76

  • Elementary Structure Theory of Lie Algebras

    Hilgert, Joachim (et al.)

    Pages 79-132

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-0-387-84794-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-0-387-84793-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-1-4899-9006-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Structure and Geometry of Lie Groups
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-387-84794-8
DOI
10.1007/978-0-387-84794-8
Hardcover ISBN
978-0-387-84793-1
Softcover ISBN
978-1-4899-9006-8
Series ISSN
1439-7382
Edition Number
1
Number of Pages
X, 746
Topics