简介：LetGbeasecondcountablelocallycompactgroupoidwithHaarsystem{λuH},HbeaclosedsubgroupoidcontainingG^0withHaarsystem{λuH}.T.MasudaintroducedtheC^*-Groupoiddynamicsystem(G,A,α)anditsreducedcrossedproductCrea(G,A)in[2]：whereAisC^*-algebraαisthekomomorphismG→Aut(A).InthispapertheauthorintroducestheC^*-groupoiddynamicsystems(H,A,α/H)and(H\G2,A,^-α)inducedby(G,A,α)andprovesthatC*red(H,A)andC^*red(H\G^2,A)arestronglyMoritaequivalentMoreovertheinducedrepresentationfromC^*red(H,A)toC^*red(G,A)isgot.

简介：ThispapercharacterizestheirrationalrotaionC^*-algebraassociatedwiththeToeplitxC^*-algebraovertheZ-shapeddomaininC^2inthesenseofthemaximalradicalseries,whichisanisomorphisminvariant.

简介：Weintroducethenotionofproperty（RD）foralocallycompact,Hausdorffandr-discretegroupoidG,andshowthatthesetS2^l（G）ofrapidlydecreasingfunctionsonGwithrespecttoacontinuouslengthfunctionIisadensespectralinvariantandFreehet＊-subalgebraofthereducedgroupoidC^＊-algebraCr^＊.（G）ofGwhenGhasproperty（RD）withrespecttol,sotheK-theoriesofbothalgebrasareisomorphicunderinclusion.EachnormalizedcoeycleconG,togetherwithaninvariantprobabilitymeasureontheunitspaceGoofG,givesrisetoacanonicalmapTconthealgebraCo（G）ofcomplexcontinuousfunctionswithcompactsupportonG.WeshowthatthemapTccanbeextendedcontinuouslytoS2^l（G）andplaysthesameroleasann-traceonCr^＊（G）whenGhasproperty（RD）andcisofpolynomialgrowthwithrespecttol,sotheConnes＇fundamentparingbetweentheK-theoryandthecycliccohomologygivesustheK-theoryinvariantsonCr^＊（G）.

简介：TheauthorsdeterminetheinvariantsoftheirrationalrotationC*-algebrasovertheLshapeddomaininC^2bythemaximalradicalseries.