Homological properties of modules over group algebras

Dales, H.G. and Polyakov, M. E. (2004) Homological properties of modules over group algebras. Proceedings of the London Mathematical Society, 89 (2). pp. 390-426. ISSN 0024-6115

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Let G be a locally compact group, and let L1 (G) be the Banach algebra which is the group algebra of G. We consider a variety of Banach left L1 (G)-modules over L1 (G), and seek to determine conditions on G that determine when these modules are either projective or injective or flat in the category. The answers typically involve G being compact or discrete or amenable. For example, in the case where G is discrete and 1 < p < ∞, we find that the module ℓp (G) is injective whenever G is amenable, and that, if it is amenable, then G is ‘pseudo-amenable’, a property very close to that of amenability.

Item Type: Journal Article
Journal or Publication Title: Proceedings of the London Mathematical Society
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2600
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 67583
Deposited By: ep_importer_pure
Deposited On: 19 Nov 2013 09:30
Refereed?: Yes
Published?: Published
Last Modified: 22 Jun 2019 06:24
URI: https://eprints.lancs.ac.uk/id/eprint/67583

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