Encyclopaedia of Mathematical Sciences

Lie Groups and Lie Algebras I

Foundations of Lie Theory Lie Transformation Groups

Authors: Gorbatsevich, V.V., Onishchik, A.L., Vinberg, E.B.

Editors: Onishchik, A.L. (Ed.)

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About this book

From the reviews:
"This volume consists of two parts. ... Part I is devoted to a systematic development of the theory of Lie groups. The Lie algebras are studied only in connection with Lie groups, i.e. a systematic study of the Lie algebras is included here. Neither the structural theory of the Lie groups and Lie algebras nor a systematic study of the topology of Lie groups form the subject of this volume. On the other hand, Part I contains a very interesting chapter on generalizations of Lie groups including very recent results. We find here Lie groups over non-archimedian fields, formal groups, infinite dimensional Lie groups and also analytic loops. Part II deals on an advanced level with actions of Lie groups on manifolds and includes subjec ts like Lie groups actions on manifolds, transitive actions, actions of compact Lie groups on low-dimensional manifolds. Though the authors state that the geometry and topology of Lie groups is almost entirely beyond the scope of this survey, one can learn a lot in these directions. Both parts are very nicely written and can be strongly recommended."
European Mathematical Society Newsletter, 1993 "... the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source... This is a hand- rather than a textbook. ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?"
The New Zealand Mathematical Society Newsletter, 1994

Table of contents (12 chapters)

Buy this book

eBook $84.99
price for USA (gross)
  • ISBN 978-3-642-57999-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-3-540-18697-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-540-61222-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lie Groups and Lie Algebras I
Book Subtitle
Foundations of Lie Theory Lie Transformation Groups
Authors
Editors
  • A.L. Onishchik
Translated by
Kozlowski, T.
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
20
Copyright
1993
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-57999-8
DOI
10.1007/978-3-642-57999-8
Hardcover ISBN
978-3-540-18697-7
Softcover ISBN
978-3-540-61222-3
Series ISSN
0938-0396
Edition Number
1
Number of Pages
VII, 238
Additional Information
Originally published as Volume 20 in the series: Encyclopaedia of Mathematical Sciences
Topics