紧李群

图书标准信息

• 作者 [美]塞潘斯基（Sepanski M. R.） 著
• 出版社 科学出版社
• 出版时间 2011-06
• 版次 1
• ISBN 9787030313911
• 定价 65.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 198页
• 字数 253千字
• 正文语种 英语
• 原版书名 Compact Lie Groups
• 丛书 国外数学名著系列

【内容简介】

《紧李群（影印版）》是“国外数学名著系列”之一，内容包括紧李群、群表示论、调和分析、李代数、阿贝尔李子群等。可供高等院校数学专业研究生、数学类科研人员学习参考。

【目录】

Preface
1CompactLieGroups
1.1BasicNotions
1.1.1Manifolds
1.1.2LieGroups
1.1.3LieSubgroupsandHomomorphisms
1.1.4CompactClassicalLieGroups
1.1.5Exercises
1.2BasicTopology
1.2.1Connectedness
1.2.2SimplyConnectedCover
1.2.3Exercises
1.3TheDoubleCoverofSO(n)
1.3.1CliffordAlgebras
1.3.2Spinn(IR)andPin
1.3.3Exercises
1.4Integration
1.4.1VolumeForms
1.4.2InvafiantIntegration
1.4.3Fubini'sTheorem
1.4.4Exercises

2Representations
2.1BasicNotions
2.1.1Definitions
2.1.2Examples
2.1.3Exercises
2.2OperationsonRepresentations
2.2.1ConstructingNewRepresentations
2.2.2IrreducibilityandSchur'sLemma
2.2.3Unitarity
2.2.4CanonicalDecomposition
2.2.5Exercises
2.3ExamplesofIrreducibility
2.3.1SU(2)andVn(C2)
2.3.2SO(n)andHarmonicPolynomials
2.3.3SpinandHalf-SpinRepresentations
2.3.4Exercises

3HarmonicAnalysis
3.1MatrixCoefficients
3.1.1SchurOrthogonality
3.1.2Characters
3.1.3Exercises
3.2Infinite-DimensionalRepresentations
3.2.1BasicDefinitionsandSchur'sLemma
3.2.2G-FiniteVectors
3.2.3CanonicalDecomposition
3.2.4Exercises
3.3ThePeter-WeylTheorem
3.3.1TheLeftandRightRegularRepresentation
3.3.2MainResult
3.3.3Applications
3.3.4Exercises
3.4FourierTheory
3.4.1Convolution
3.4.2PlancherelTheorem
3.4.3ProjectionOperatorsandMoreGeneralSpaces
3.4.4Exercises

4LieAlgebras
4.1BasicDefinitions
4.1.1LieAlgebrasofLinearLieGroups
4.1.2ExponentialMap
4.1.3LieAlgebrasfortheCompactClassicalLieGroups
4.1.4Exercises
4.2FurtherConstructions
4.2.1LieAlgebraHomomorphisms
4.2.2LieSubgroupsandSubalgebras
4.2.3CoveringHomomorphisms
4.2.4Exercises

5AbelianLieSubgroupsandStructure
5.1AbelianSubgroupsandSubalgebras
5.1.1MaximalToriandCaftanSubalgebras
5.1.2Examples
5.1.3ConjugacyofCartanSubalgehras
5.1.4MaximalTorusTheorem
5.1.5Exercises
5.2Structure
5.2.1ExponentialMapRevisited
5.2.2LieAlgebraStructure
5.2.3CommutatorTheorem
5.2.4CompactLieGroupStructure
5.2.5Exercises

6RootsandAssociatedStructures
6.1RootTheory
6.1.1RepresentationsofLieAlgebras
6.1.2ComplexificationofLieAlgebras
6.1.3Weights
6.1.4Roots
6.1.5CompactClassicalLieGroupExamples
6.1.6Exercises
6.2TheStandards[(2,C)Triple
6.2.1CartanInvolution
6.2.2KillingForm
6.2.3TheStandardsl(2,C)andsu(2)Triples
6.2.4Exercises
6.3Lattices
6.3.1Definitions
6.3.2Relations
6.3.3CenterandFundamentalGroup
6.3.4Exercises
6.4WeylGroup
6.4.1GroupPicture
6.4.2ClassicalExamples
6.4.3SimpleRootsandWeylChambers
6.4.4TheWeylGroupasaReflectionGroup
6.4.5Exercises

7HighestWeightTheory
7.1HighestWeights
7.1.1Exercises
7.2WeylIntegrationFormula
7.2.1RegularElements
7.2.2MainTheorem
7.2.3Exercises
7.3WeylCharacterFormula
7.3.1Machinery
7.3.2MainTheorem
7.3.3WeylDenominatorFormula
7.3.4WeylDimensionFormula
7.3.5HighestWeightClassification
7.3.6FundamentalGroup
7.3.7Exercises
7.4Borel-WeilTheorem
7.4.1InducedRepresentations
7.4.2ComplexStructureonG/T
7.4.3HolomorphicFunctions
7.4.4MainTheorem
7.4.5Exercises
References
Index