## Second cohomology group of group algebras with coefficients in iterated duals

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- by A. Pourabbas
- Proc. Amer. Math. Soc.
**132**(2004), 1403-1410 - DOI: https://doi.org/10.1090/S0002-9939-03-07219-8
- Published electronically: August 28, 2003
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## Abstract:

In this paper we show that the first cohomology group $\mathcal {H}^1(\ell ^1(G),(\ell ^1(S))^{(n)})$ is zero for every odd $n\in \mathbb {N}$ 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 $\mathcal {H}^2(\ell ^1(G),(\ell ^1(S))^{(n)})$ is a Banach space. Finally, for every locally compact group $G$ we show that $\mathcal {H}^2(L^1(G),(L^1(G))^{(n)})$ is a Banach space for every odd $n\in \mathbb {N}$.## References

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## Bibliographic Information

**A. Pourabbas**- Affiliation: Faculty of Mathematics and Computer Science, Amirkabir University, 424 Hafez Avenue, Tehran 15914, Iran
- Email: arpabbas@aut.ac.ir
- Received by editor(s): January 14, 2002
- Received by editor(s) in revised form: December 31, 2002
- Published electronically: August 28, 2003
- Additional Notes: This research was supported by a grant from Amir Kabir University. The author would like thank the Institute for their kind support.
- Communicated by: Joseph A. Ball
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**132**(2004), 1403-1410 - MSC (2000): Primary 43A20; Secondary 46M20
- DOI: https://doi.org/10.1090/S0002-9939-03-07219-8
- MathSciNet review: 2053346