Some results on the Hochschild cohomology of group algebras

Abstract

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