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Some results on the Hochschild cohomology of group algebras

Authors:	A Pourabbas

Institution:	Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, Iran

Abstract:	In this paper we investigate structure of the second cohomology of a discrete group . First, for a -set we show that an isomorphism of vector spaces from $\mathcal{H}^n(\ell^1(G),\ell^\infty(S))$ onto $\bigoplus_{i\in I}^\infty \mathcal{H}^n(\ell^1(G),\ell^\infty({\mathcal{C}_i}))$ exists, where $\{\mathcal{C}_{i}\}_{i\in I}$ is the set of orbits of . 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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