Hochschild Cohomology of Factors with Property $Γ$

Erik Christensen; Florin Pop; Allan Sinclair; Roger Smith

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Hochschild Cohomology of Factors with Property $Γ$

Erik Christensen·Florin Pop·Allan Sinclair·Roger Smith

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Abstract

The main result of this paper is that the k^{\rm th} continuous Hochschild cohomology groups H^k(\cl M,\cl M) and H^k(\cl M,B(H)) of a von Neumann factor ${\cl M}\subseteq B(H) of type {\rm II}_1 with property Gamma are zero for all positive integers k. The method of proof involves the construction of hyperfinite subfactors with special properties and a new inequality of Grothendieck type for multilinear maps. We prove joint continuity in the $\|\cdot\|_2$-norm of separately ultraweakly continuous multilinear maps, and combine these results to reduce to the case of completely bounded cohomology which is already solved.

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BibTeX RIS

Erik Christensen, Florin Pop, Allan Sinclair, Roger Smith. 2004-04-20. Hochschild Cohomology of Factors with Property $Γ$. https://arxiv.org/abs/math/0107078

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