朴素李理论

图书标准信息

• 作者 [美]史迪威 著
• 出版社 世界图书出版公司
• 出版时间 2012-01
• 版次 1
• ISBN 9787510040597
• 定价 29.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 218页

【内容简介】

《朴素李理论(影印版)》，本书是一部介绍李群和李代数的本科生教程，基本的微积分和线性代数知识将对理解本书十分重要。

【目录】

1Geometryofcomplexnumbersandquaternions

1．1Rotationsoftheplane

1．2Matrixrepresentationofcomplexnumbers

1．3Quaternions

1．4Consequencesofmultiplicativeabsolutevalue

1．5Quaternionrepresentationofspacerotations

1．6Discussion

2Groups

2．1Crashcourseongroups

2．2Crashcourseonhomomorphisms

2．3ThegroupsSU(2)andSO(3)

2．4IsometricsofR''andreflections

2．5RotationsofR4andpairsofquaternions

2．6Directproductsofgroups

2．7ThemapfromSU(2)SU(2)toSO(4)

2．8Discussion

3Generalizedrotationgroups

3．1Rotationsasorthogonaltransformations

3．2Theorthogonaiandspecialorthogonalgroups

3．3Theunitarygroups

3．4Thesymplecticgroups

3．5Maximaltoriandcenters

3．6MaximaltoriinSO(n)，U(n)，SU(n)，Sp(n)

3．7CentersofSO(n)，U(n)，SU(n)，Sp(n)

3．8Connectcdnessanddiscreteness

3．9Discussion

4Theexponentialmap

4．1TheexponentialmapontoSO(2)

4．2TheexponentialmapontoSU(2)

4．3ThetangentspaceofSU(2)

4．4TheLiealgebrasu(2)ofSU(2)

4．5Theexponentialofasquarematrix

4．6Theaffinegroupoftheline

4．7Discussion

5Thetangentspace

5．1TangentvectorsofO(n)，U(n)，Sp(n)

5．2ThetangentspaceofSO(n)

5．3ThetangentspaceofU(n)，SU(n)，Sp(n)

5．4Algebraicpropertiesofthetangentspace

5．5DimensionofLiealgebras

5．6Complexification

5．7QuaternionLiealgebras

5．8Discussion

6StructureofLiealgebras

6．1Normalsubgroupsandideals

6．2Idealsandhomomorphisms

6．3Classicalnon-simpleLiealgebras

6．4Simplicityof(n，C)andsu(n)

6．5Simplicityofo(n)forn>4

6．6Simplicityofp(n)

6．7Discussion

7Thematrixlogarithm

7．1Logarithmandexponential

7．2Theexpfunctiononthetangentspace

7．3Limitpropertiesoflogandexp

7．4Thelogfunctionintothetangentspace

7．5SO(n)，SU(n)，andSp(n)revisited

7．6TheCampbell-Baker-Hausdorfftheorem

7．7Eichler'sproofofCampbell-Baker-Hausdorff

7，8Discussion

8Topology

8．1OpenandclosedsetsinEuclideanspace

8．2Closedmatrixgroups

8．3Continuousfunctions

8．4Compactsets

8．5Continuousfunctionsandcompactness

8．6Pathsandpath-connectedness

8．7Simpleconnectedness

8．8Discussion

9SimplyconnectedLiegroups

9．1ThreegroupswithtangentspaceR

9．2Threegroupswiththecross-productLiealgebra

9．3Liehomomorphisms

9．4Uniformcontinuityofpathsanddeformations

9．5Deformingapathinasequenceofsmallsteps

9．6LiftingaLiealgebrahomomorphism

9．7Discussion

Bibliography

Index