Skip to main content
  • Book
  • © 1993

Lie Groups and Lie Algebras I

Foundations of Lie Theory Lie Transformation Groups

Editors:

(view affiliations)

Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 20)

Buying options

eBook
USD 89.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-57999-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 119.99
Price excludes VAT (USA)
Hardcover Book
USD 159.99
Price excludes VAT (USA)

This is a preview of subscription content, access via your institution.

Table of contents (12 chapters)

  1. Front Matter

    Pages i-vii
  2. Foundations of Lie Theory

    1. Front Matter

      Pages 1-1
    2. Introduction

      • A. L. Onishchik
      Pages 4-5
    3. Basic Notions

      • A. L. Onishchik
      Pages 6-29
    4. The Universal Enveloping Algebra

      • A. L. Onishchik
      Pages 59-74
    5. Generalizations of Lie Groups

      • A. L. Onishchik
      Pages 74-94
  3. Lie Transformation Groups

    1. Front Matter

      Pages 95-95
    2. Introduction

      • A. L. Onishchik
      Pages 99-99
    3. Lie Group Actions on Manifolds

      • A. L. Onishchik
      Pages 100-120
    4. Transitive Actions

      • A. L. Onishchik
      Pages 121-149
    5. Actions of Compact Lie Groups

      • A. L. Onishchik
      Pages 149-160
    6. Compact Homogeneous Spaces

      • A. L. Onishchik
      Pages 172-210
  4. Back Matter

    Pages 231-238

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

Keywords

  • YellowSale2006
  • algebra
  • automorphism
  • derivation
  • Dimension
  • lie group
  • manifold
  • ring homomorphism
  • topological group
  • transformation group

Editors and Affiliations

  • Yaroslavl University, Yaroslavl, Russia

    A. L. Onishchik

Bibliographic Information

Buying options

eBook
USD 89.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-57999-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 119.99
Price excludes VAT (USA)
Hardcover Book
USD 159.99
Price excludes VAT (USA)