Vanishing of 𝐻²_{𝑤}(𝑀,𝐾(𝐻)) for certain finite von Neumann algebras

Rădulescu, Florin

doi:10.1090/S0002-9947-1991-1031241-X

Vanishing of $H^ 2_ w(M,K(H))$ for certain finite von Neumann algebras
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Trans. Amer. Math. Soc. 326 (1991), 569-584 Request permission

Abstract:

We prove the vanishing of the second Hochschild cohomology group $H_w^2 (M,K(H))$, whenever $M \subset B(H)$ is a finite countably decomposable von Neumann algebra not containing a non $\Gamma$-factor or a factor without Cartan subalgebra as a direct summand. Here $H$ is a Hubert space, and $K(H)$ the compact operators.

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