Some results on the Hochschild cohomology of group algebras

Pourabbas, A.

doi:10.1090/S0002-9939-07-08705-9

Some results on the Hochschild cohomology of group algebras
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Proc. Amer. Math. Soc. 135 (2007), 2095-2105 Request permission

Abstract:

In this paper we investigate structure of the second cohomology of a discrete group $G$. First, for a $G$-set $S$ we show that an isomorphism of vector spaces from $\mathcal {H}^n(\ell ^1(G),\ell ^\infty (S))$ onto $\bigoplus _{i\in I}^\infty \mathcal {H}^n(\ell ^1(G),\ell ^\infty (\mathbb {C}))$ exists, where $\{\mathcal {C}_{i}\}_{i\in I}$ is the set of orbits of $S$. Next we define the notion of pseudoderivation and apply it for the calculation of $\mathcal {H}_{b,2}^2(\ell ^1(G),\ell ^\infty (S))$.

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