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In this paper we show that the first cohomology group H 1 (l 1 (G), (l 1 (S)) (n) ) is zero for every odd n E N and for every G-set S. In the case when G is a discrete group, this is a generalization of the following result of Dales et al.: for any locally compact group G, L 1 (G) is (2n + 1)-weakly amenable. Next we show that the second cohomology group H 2 (l 1 (G), (l 1 (S)) (n) ) is a Banach space. Finally, for every locally compact group G we show that H 2 (L 1 (G), (L 1 (G) (n) ) is a Banach space for every odd n ∈ N.

Second cohomology group of group algebras with coefficients in iterated duals