Stability of Lie groupoid -algebras

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• 作者：Claire Debord^a ; ^{claire.debord@math.univ-bpclermont.fr" class="auth_mail" title="E-mail the corresponding author} ; Georges Skandalis^b ; ^{skandalis@math.univ-paris-diderot.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 58H05 ; secondary ; 46L89 ; 58J22
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：105
• 期：Complete
• 页码：66-74
• 全文大小：440 K

文摘

In this paper we generalize a theorem of M. Hilsum and G. Skandalis stating that the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0393044016300547&_mathId=si1.gif&_user=111111111&_pii=S0393044016300547&_rdoc=1&_issn=03930440&md5=82cd2e14591605661a989e1a5b5bc416" title="Click to view the MathML source">C^∗class="mathContainer hidden">class="mathCode">$C^{\ast }$-algebra of any foliation of nonzero dimension is stable. Precisely, we show that the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0393044016300547&_mathId=si1.gif&_user=111111111&_pii=S0393044016300547&_rdoc=1&_issn=03930440&md5=82cd2e14591605661a989e1a5b5bc416" title="Click to view the MathML source">C^∗class="mathContainer hidden">class="mathCode">$C^{\ast }$-algebra of a Lie groupoid is stable whenever the groupoid has no orbit of dimension zero. We also prove an analogous theorem for singular foliations for which the holonomy groupoid as defined by I. Androulidakis and G. Skandalis is not Lie in general.