On unbounded, non-trivial Hochschild cohomology in finite von Neumann algebras and higher order Berezin's quantization

Florin Radulescu

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arXiv · 1309.1377

On unbounded, non-trivial Hochschild cohomology in finite von Neumann algebras and higher order Berezin's quantization

Florin Radulescu

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Abstract

We introduce a class of densely defined, unbounded, 2-Hochschild cocycles ([PT]) on finite von Neumann algebras $M$. Our cocycles admit a coboundary, determined by an unbounded operator on the standard Hilbert space associated to the von Neumann algebra $M$. For the cocycles associated to the $Γ$-equivariant deformation ([Ra]) of the upper halfplane $(Γ=PSL_2(\mathbb Z))$, the "imaginary" part of the coboundary operator is a cohomological obstruction - in the sense that it can not be removed by a "large class" of closable derivations, with non-trivial real part, that have a joint core domain, with the given coboundary.

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Florin Radulescu. 2014-08-16. On unbounded, non-trivial Hochschild cohomology in finite von Neumann algebras and higher order Berezin's quantization. https://arxiv.org/abs/1309.1377

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