Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hochschild cohomology of type II$_1$ von Neumann algebras with Property
  $\Gamma$   In this paper, Property $\Gamma$ for a type II$_{1}$ von Neumann algebra is
introduced as a generalization of Murray and von Neumann's Property $\Gamma$
for a type II$_{1}$ factor. The main result of this paper is that if a type
II$_{1}$ von Neumann algebra $\mathcal{M}$ with separable predual has Property
$\Gamma$, then the continuous Hochschild cohomology group $H^{k}(\mathcal{M},
\mathcal{M})$ vanishes for every $k \geq 2$. This gives a generalization of an
earlier result due to E. Christensen, F. Pop, A.M. Sinclair and R.R. Smith.

16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom