李群论（英文版）

图书标准信息

• 作者 [美]科沃里（Claude Chevalley） 著
• 出版社 世界图书出版公司
• 出版时间 2013-01
• 版次 1
• ISBN 9787510050657
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 213页
• 正文语种 英语

【内容简介】

　　ExpositorybooksonthetheoryofLiegroupsgenerallyconfinethemselvestothelocalaspectofthetheory.Thislimitationwasprobablynecessaryaslongasgeneraltopologywasnotyetsufficientlywellelaboratedtoprovideasolidbaseforatheoryinthelarge.Thesedaysarenowpassed，andwehavethoughtthatitwouldbe'usefultohaveasystematictreatmentofthetheoryfromaglobalpointofview.ThepresentvolumeintroducesthemainbasicprincipleswhichgovernthetheoryofLiegroups.
　　ALiegroupisatthesametimeagroup，atopologicalspaceandamanifold:ithasthereforethreekindsof"structures，"whichareinterrelatedwitheachother.Theelem，entarypropertiesofabstractgroupsarebynowsufficientlywellknowntothegeneralmathematicalpublictomakeitunnecessaryforsuchabookasthisonetocontainapurelygroup-theoreticchapter.Thetheoryoftopologicalgroups，however，hasbeenincludedandistreatedinChapterII.Thegreat-estpartofthischapterisconcernedwiththetheoryofcoveringspacesandgroups，whichisdevelopedindependentlyfromthetheoryofpaths.ChapterIIIisconcernedwiththetheoryof（analytic）mani-folds（independentlyofthenotionofgroup）.OurdefinitionofamanifoldisinspiredbythedefinitionofaRiemannsurfacegivenbyH.Weylinhisbook。‘DieIdeederRiemannschenFlache";ithas，comparedwiththedefinitionbyoverlappingsystemofcoordinates，theadvantageofbeingintrinsic.Thetheoryofinvolutivesystemsofdifferentialequationsonamanifoldistreatednotonlyfromthelocalpointofviewbutalsointhelarge.Inordertoachievethis，adefini-tionofthesubmanifoldsofamanifoldisgivenaccordingtowhichasubmanifoldisnotnecessarilyatopologicalsubspaceofthemanifoldinwhichitisimbedded.

【目录】

INTRODCTION
Ⅰ.THECLASSICALLINEARGROUPS
Ⅱ.TOPOLIGIVALGROUPS
Ⅲ.MANIFOLDS
Ⅳ.ANAKYTICGROUPS.LIEGROUPS
Ⅴ.THEDIFFERENTIALCALCULUSOFCARTAN
Ⅵ.COMPACTLIEANDTHEIRREPRESENTATIONG
INDEX