Type III factors with unique Cartan decomposition

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• 作者：Cyril Houdayer ; Stefaan Vaes
• 关键词：46L10 ; 46L54 ; 37A40
• 刊名：Journal des Mathematiques Pures et Appliquees
• 出版年：2013
• 出版时间：October, 2013
• 年：2013
• 卷：100
• 期：4
• 页码：564-590
• 全文大小：367 K

文摘

We prove that for any free ergodic nonsingular nonamenable action of all ¦£ in a large class of groups including all hyperbolic groups, the associated group measure space von Neumann algebra has as its unique Cartan subalgebra, up to unitary conjugacy. This generalizes the probability measure preserving case that was established in Popa and Vaes (in press) . We also prove primeness and indecomposability results for such crossed products, for the corresponding orbit equivalence relations and for arbitrary amalgamated free products over a subalgebra B of type I.