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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Gorbatsevich, V.V. Foundations of Lie theory and Lie transformation groups (DLC) 98193499 (OCoLC)37019252 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
V V Gorbatsevich; A L Onishchik; Ė B Vinberg |

ISBN: | 9783642579998 364257999X |

OCLC Number: | 883392233 |

Language Note: | Translated from the Russian by A. Kozlowski. |

Notes: | "Second printing 1997 of the first edition 1993, which was originally published as Lie groups and Lie algebras I, volume 20 of the Encyclopaedia of mathematical sciences"--Title page verso. Translated from the Russian by A. Kozlowski. |

Description: | 1 online resource (235 pages) |

Contents: | Foundations of Lie theory / A.L. Onishchik, E.B. Vinberg -- Lie transformation groups / V.V. Gorbatsevich, A.L. Onishchik. |

Other Titles: | Lie groups and Lie algebras. |

Responsibility: | V.V. Gorbatsevich, A.L. Onishchik, E.B. Vinberg. |

More information: |

### Abstract:

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.

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