The nuclear dimension of C^⁎-algebras associated to homeomorphisms

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• 作者：Ilan Hirshberg^a ; ^{ilan@math.bgu.ac.il" class="auth_mail" title="E-mail the corresponding author} ; Jianchao Wu^b ; ^{jianchao.wu@uni-muenster.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：C⁎C⁎-algebras ; Nuclear dimension ; C⁎C⁎-dynamics
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：2 January 2017
• 年：2017
• 卷：304
• 期：Complete
• 页码：56-89
• 全文大小：562 K

文摘

We show that if X   is a finite dimensional locally compact Hausdorff space, then the crossed product of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870815301250&_mathId=si1.gif&_user=111111111&_pii=S0001870815301250&_rdoc=1&_issn=00018708&md5=ad46c035c5203d152dcf56dc1f54ecbe" title="Click to view the MathML source">C₀(X)class="mathContainer hidden">class="mathCode">$C_0(X)$ by any automorphism has finite nuclear dimension. This generalizes previous results, in which the automorphism was required to be free. As an application, we show that group class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870815301250&_mathId=si2.gif&_user=111111111&_pii=S0001870815301250&_rdoc=1&_issn=00018708&md5=b8deeaf9c47ba11ff8fb57d62af08b60" title="Click to view the MathML source">C^⁎class="mathContainer hidden">class="mathCode">$C^{⁎}$-algebras of certain non-nilpotent groups have finite nuclear dimension.