Hostname: page-component-5cf477f64f-r2nwp Total loading time: 0 Render date: 2025-04-04T22:55:38.243Z Has data issue: false hasContentIssue false
  • English
  • Français

ON HOMOLOGICAL PROPERTIES FOR SOME MODULES OF UNIFORMLY CONTINUOUS FUNCTIONS OVER CONVOLUTION ALGEBRAS

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

Published online by Cambridge University Press:  13 July 2011

RASOUL NASR-ISFAHANI  and
SIMA SOLTANI RENANI
RASOUL NASR-ISFAHANI*
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email: isfahani@cc.iut.ac.ir)
SIMA SOLTANI RENANI
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email: simasoltani@cc.iut.ac.ir)
*
✉For correspondence; e-mail: isfahani@cc.iut.ac.ir
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For a locally compact group G, let LUC(G) denote the space of all left uniformly continuous functions on G. Here, we investigate projectivity, injectivity and flatness of LUC(G) and its dual space LUC(G)* as Banach left modules over the group algebra as well as the measure algebra of G.

Keywords

amenabilityflatnessinjectivityprojectivityBanach modulelocally compact group

MSC classification

Secondary: 43A07: Means on groups, semigroups, etc.; amenable groups 43A20: $L^1$-algebras on groups, semigroups, etc. 46H05: General theory of topological algebras 46H25: Normed modules and Banach modules, topological modules (if not placed in or )
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 2 , October 2011 , pp. 177 - 185
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Bahrami, F., Nasr-Isfahani, R. and Soltani Renani, S., ‘Homological properties of certain Banach modules over group algebras’, Proc. Edinb. Math. Soc. (2) 54 (2011), 321–328.CrossRefGoogle Scholar
[2]Dales, H. G. and Polyakov, M. E., ‘Homological properties of modules over group algebras’, Proc. Lond. Math. Soc. (3) 89 (2004), 390–426.CrossRefGoogle Scholar
[3]Helemskii, A. Ya., The Homology of Banach and Topological Algebras (Kluwer Academic Publishers Group, Dordrecht, 1989).CrossRefGoogle Scholar
[4]Hewitt, E. and Ross, K., Abstract Harmonic Analysis II (Springer, New York, 1970).Google Scholar
[5]Johnson, B. E., Cohomology in Banach Algebras, Memoirs of the American Mathematical Society, 127 (American Mathematical Society, Providence, RI, 1972).CrossRefGoogle Scholar
[6]Lau, A. T. and Losert, V., ‘Complementation of certain subspaces of L ∞(G) of a locally compact group’, Pacific J. Math. 141 (1990), 295–310.CrossRefGoogle Scholar
[7]Nasr-Isfahani, R. and Soltani Renani, S., ‘Character contractibility of Banach algebras and homological properties of Banach modules’, Studia Math. 202 (2011), 205–225.CrossRefGoogle Scholar
[8]Pier, J. P., Amenable Locally Compact Groups, Pure and Applied Mathematics (John Wiley and Sons, New York, 1984).Google Scholar
[9]White, M. C., ‘Injective module for uniform algebras’, Proc. Lond. Math. Soc. (3) 73 (1996), 155–184.CrossRefGoogle Scholar