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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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