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Homological properties of certain Banach modules over group algebras

Part of: Topological algebras, normed rings and algebras, Banach algebras Abstract harmonic analysis

Published online by Cambridge University Press:  07 April 2011

Farid Bahrami ,
Rasoul Nasr-Isfahani  and
Sima Soltani Renani
Farid Bahrami
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (fbahrami@cc.iut.ac.ir; isfahani@cc.iut.ac.ir; simasoltani@math.iut.ac.ir)
Rasoul Nasr-Isfahani
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (fbahrami@cc.iut.ac.ir; isfahani@cc.iut.ac.ir; simasoltani@math.iut.ac.ir)
Sima Soltani Renani
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (fbahrami@cc.iut.ac.ir; isfahani@cc.iut.ac.ir; simasoltani@math.iut.ac.ir)
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Abstract

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Homological properties of several Banach left L1(G)-modules have been studied by Dales and Polyakov and recently by Ramsden. In this paper, we characterize some homological properties of and as Banach left L1(G)-modules, such as flatness, injectivity and projectivity.

Keywords

amenabilityBanach moduleflatnessinjectivityprojectivitylocally compact group

MSC classification

Secondary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 43A20: $L^1$-algebras on groups, semigroups, etc. 46H25: Normed modules and Banach modules, topological modules (if not placed in or )
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 2 , June 2011 , pp. 321 - 328
Copyright
Copyright © Edinburgh Mathematical Society 2011

References

1.Dales, H. G., Banach algebras and automatic continuity, London Mathematical Society Monographs, Volume 24 (Clarendon, Oxford, 2000).Google Scholar
2.Dales, H. G. and Polyakov, M. E., Homological properties of modules over group algebras, Proc. Lond. Math. Soc. 89 (2004), 390–426.CrossRefGoogle Scholar
3.Helemskii, A. Ya., The homology of Banach and topological algebras (Kluwer, Dordrecht, 1989).CrossRefGoogle Scholar
4.Helemskii, A. Ya., Banach and locallly convex algebras (Clarendon, Oxford, 1993).CrossRefGoogle Scholar
5.Hewitt, E. and Ross, K., Abstract harmonic analysis, Volume II (Springer, 1970).Google Scholar
6.Isik, N., Pym, J. and Ulger, A., The second dual of the group algebra of a compact group, J. Lond. Math. Soc. 35 (1987), 135–148.CrossRefGoogle Scholar
7.Lau, A. T. and Pym, J., Concerning the second dual of the group algebra of a locally compact group, J. Lond. Math. Soc. 41 (1990), 445–460.Google Scholar
8.Ramsden, P., Homological properties of semigroup algebras, PhD thesis, University of Leeds (2008).Google Scholar
9.Runde, V., Lectures on amenability, Lecture Notes in Mathematics, Volume 1774 (Springer, 2002).CrossRefGoogle Scholar