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Hochschild cohomology of II1 factors with Cartan maximal abelian subalgebras

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  28 May 2009

Jan M. Cameron
Jan M. Cameron
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA; Email: (jcameron@math.tamu.edu)
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Abstract

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In this paper we prove that, for a type-II1 factor N with a Cartan maximal abelian subalgebra, the Hochschild cohomology groups Hn(N,N)=0 for all n≥1. This generalizes the result of Sinclair and Smith, who proved this for all N having a separable predual.

Keywords

Cartan subalgebrasnormalizersHochschild cohomologyfinite factors

MSC classification

Secondary: 46L10: General theory of von Neumann algebras
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 2 , June 2009 , pp. 287 - 295
Copyright
Copyright © Edinburgh Mathematical Society 2009