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Some results on the Hochschild cohomology of group algebras

Author: A. Pourabbas
Journal: Proc. Amer. Math. Soc. 135 (2007), 2095-2105
MSC (2000): Primary 43A20; Secondary 46M20
Published electronically: February 2, 2007
MathSciNet review: 2299486
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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({\mathcal{C}_i}))$ 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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Additional Information

A. Pourabbas
Affiliation: Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, Iran

Received by editor(s): February 23, 2005
Received by editor(s) in revised form: March 9, 2006
Published electronically: February 2, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society

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