Second cohomology group of group algebras with coefficients in iterated duals
Author:
A. Pourabbas
Journal:
Proc. Amer. Math. Soc. 132 (2004), 14031410
MSC (2000):
Primary 43A20; Secondary 46M20
Published electronically:
August 28, 2003
MathSciNet review:
2053346
Fulltext PDF Free Access
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Abstract: In this paper we show that the first cohomology group is zero for every odd and for every set . In the case when is a discrete group, this is a generalization of the following result of Dales et al.: for any locally compact group , is weakly amenable. Next we show that the second cohomology group is a Banach space. Finally, for every locally compact group we show that is a Banach space for every odd .
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Additional Information
A. Pourabbas
Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University, 424 Hafez Avenue, Tehran 15914, Iran
Email:
arpabbas@aut.ac.ir
DOI:
http://dx.doi.org/10.1090/S0002993903072198
PII:
S 00029939(03)072198
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
Article copyright:
© Copyright 2003
American Mathematical Society
