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LIE GROUPSPDF|Epub|txt|kindle电子书版本网盘下载
- PRENTICE-HALL 著
- 出版社： INC.
- ISBN：
- 出版时间：1974
- 标注页数：0页
- 文件大小：84MB
- 文件页数：439页
- 主题词：
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图书目录
Chapter 1 Differentiable and Analytic Manifolds1
1.1 Differentiable Manifolds1
1.2 Analytic Manifolds20
1.3 The Frobenius Theorem25
1.4 Appendix31
Exercises35
Chapter 2 Lie Groups and Lie Algebras41
2.1 Definition and Examples of Lie Groups41
2.2 Lie Algebras46
2.3 The Lie Algebra of a Lie Group51
2.4 The Enveloping Algebra of a Lie Group55
2.5 Subgroups and Subalgebras57
2.6 Locally isomorphic Groups61
2.7 Homomorphisms67
2.8 The Fundamental Theorem of Lie72
2.9 Closed Lie Subgroups and Homogeneous Spaces.Orbits and Spaces of Orbits74
2.10 The Exponential Map84
2.11 The Uniqueness of the Real Analytic Structure of a Real Lie Group92
2.12 Taylor Series Expansions on a Lie Group94
2.13 The Adjoint Representations of ？and G101
2.14 The Differential of the Exponential Map107
2.15 The Baker-Campbell-Hausdorff Formula114
2.16 Lie’s Theory of Transformation Groups121
Exercises133
Chapter 3 Structure Theory149
3.1 Review of Linear Algebra149
3.2 The Universal Enveloping Algebra of a Lie Algebra166
3.3 The Universal Enveloping Algebra as a Filtered Algebra176
3.4 The Enveloping Algebra of a Lie Group184
3.5 Nilpotent Lie Algebras189
3.6 Nilpotent Analytic Groups195
3.7 Solvable Lie Algebras200
3.8 The Radical and the Nil Radical204
3.9 Cartan’s Criteria for Solvability and Semisimplicity207
3.10 Semisimple Lie Algebras213
3.11 The Casimir Element216
3.12 Some Cohomology219
3.13 The Theorem of Weyl222
3.14 The Levi Decomposition224
3.15 The Analytic Group of a Lie Algebra228
3.16 Reductive Lie Algebras230
3.17 The Theorem of Ado233
3.18 Some Global Results238
Exercises247
Chapter 4 Complex Semisimple Lie Algebras And Lie Groups：Structure and Representation260
4.1 Cartan Subalgebras260
4.2 The Representations of ？？（2，C）.267
4.3 Structure Theory273
4.4 The Classical Lie Algebras293
4.5 Determination of the Simple Lie Algebras over C305
4.6 Representations with a Highest Weight313
4.7 Representations of Semisimple Lie Algebras324
4.8 Construction of a Semisimple Lie Algebra from its Cartan Matrix329
4.9 The Algebra of Invariant Polynomials on a Semisimple Lie Algebra333
4.10 Infinitesimal Characters337
4.11 Compact and Complex Semisimple Lie Groups342
4.12 Maximal Tori of Compact Semisimple Groups351
4.13 An Integral Formula356
4.14 The Character Formula of H.Weyl364
4.15 Appendix.Finite Reflection Groups369
Exercises387
Bibliography417
Index423