Title | Lie Groups and Lie Algebras I [electronic resource] : Foundations of Lie Theory Lie Transformation Groups / edited by A. L. Onishchik |
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Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1993 |

Connect to | http://dx.doi.org/10.1007/978-3-642-57999-8 |

Descript | VII, 238 p. online resource |

SUMMARY

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

CONTENT

I.Foundations of Lie Theory -- 1. Basic Notions -- 2. The Relation Between Lie Groups and Lie Algebras -- 3. The Universal Enveloping Algebra -- 4. Generalizations of Lie Groups -- II. Lie Transformation Groups -- 1. Lie Group Actions on Manifolds -- 2. Transitive Actions -- 3. Actions of Compact Lie Groups -- 4. Homogeneous Spaces of Nilpotent and Solvable Groups -- 5. Compact Homogeneous Spaces -- 6. Actions of Lie Groups on Low-dimensional Manifolds

Mathematics
Algebraic geometry
Topological groups
Lie groups
Differential geometry
Algebraic topology
Manifolds (Mathematics)
Complex manifolds
Mathematics
Topological Groups Lie Groups
Differential Geometry
Manifolds and Cell Complexes (incl. Diff.Topology)
Algebraic Topology
Algebraic Geometry