最 低 价：￥33.80
定 价：￥69.00
作 者：(美)范阮达若詹/(美国)(V.S.Varadarajan)范阮达若詹/V. S. Varadarajan 著
出 版 社：世界图书出版公司
出版时间：2008-05
I S B N：9787506292245
| The standard books on Lie theory begin immediately with the general case:a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time. Furthermore, with this approach, one must either assume the reader is familiar with the theory of differentiable manifolds （which rules out a substantial part of one‘s audience） or one must spend considerable time at the beginning of the book explaining this theory （in which case, it takes a long time to get to Lie theory proper）. |
| Preface Chapter 1 Differentiable and Analytic Manifolds 1.1 Differentiable Manifolds 1.2 Analytic Manifolds 1.3 The Frobcnius Theorem 1.4 Appendix Exercises Chapter 2 Lie Groups and Lie Algebras 2.1 Definition and Examples of Lie Groups 2.2 Lie Algebras 2.3 The Lie Algebra of a Lie Group 2.4 The Enveloping Algebra of a Lie Group 2.5 Subgroups and Subalgebras 2.6 Locally isomorphic Groups 2.7 Homomorphisms 2.8 The Fundamental Theorem of Lie 2.9 Closed Lie Subgroups and Homogeneous Spaces. Orbits and Spaces of Orbits 2.10 The Exponential Map 2.11 The Uniqueness of the Real Analytic Structure of a& |
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