an introduction to noncommutative spaces and their geometry 186s landi

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1、AnIntroductiontoNoncommutativeSpacesandtheirGeometryGiovanniLandiDipartimentodiScienzeMatematiche,UniversitadiTrieste,P.leEuropa1,I-34127,Trieste,Italia.INFN,SezionediNapoli,Mostrad'Oltremarepad.20,I-80125,Napoli,Italia.Trieste,January16,1997hep-th/9701078hep-th/9701

2、07816Jan1997Contents1Introduction12NoncommutativeSpacesandAlgebrasofFunctions52.1Algebras.....................................52.2CommutativeSpaces..............................92.3NoncommutativeSpaces............................112.3.1TheJacobson(orhull-kernel)Topolo

3、gy................122.4CompactOperators...............................163NoncommutativeLattices193.1TheTopologicalApproximation........................193.2OrderandTopology..............................213.3HowtoRecovertheSpaceBeingApproximated...............263.4Nonc

4、ommutativeLattices...........................313.4.1ThespacePrimAasaPoset.....................333.4.2AF-Algebras...............................333.4.3FromBratteliDiagramstoNoncommutativeLattices........403.4.4FromNoncommutativeLatticestoBratteliDiagrams........433.5Ho

5、wtoRecovertheAlgebraBeingApproximated..............543.6OperatorValuedFunctionsonNoncommutativeLattices..........554ModulesasBundles574.1Modules.....................................574.2ProjectiveModulesofFiniteType.......................594.3HermitianStructuresoverPr

6、ojectiveModules................624.4FewElementsofK-theory...........................634.4.1TheGroupK0.............................644.4.2TheK-theoryofthePenroseTiling..................684.4.3HigherOrderK-groups.........................725TheSpectralCalculus755.1Innit

7、esimals..................................75i5.2TheDixmierTrace...............................765.3WodzickiResidueandConnes'TraceTheorem................815.4SpectralTriples.................................855.5TheCanonicalTripleoveraManifold.....................865.6Di

8、stanceandIntegralforaSpectralTriple..................905.7RealSpectralTriples..............................915.8ATwoPointsSp