Homological Properties of Modules Over Group Algebras |
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Authors: | Dales H G; Polyakov M E |
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Institution: | Department of Pure Mathematics, University of Leeds Leeds LS2 9JT, United Kingdom. E-mail: garth{at}maths.leeds.ac.uk |
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Abstract: | Let G be a locally compact group, and let L1 (G) be the Banachalgebra which is the group algebra of G. We consider a varietyof Banach left L1 (G)-modules over L1 (G), and seek to determineconditions on G that determine when these modules are eitherprojective or injective or flat in the category. The answerstypically involve G being compact or discrete or amenable. Forexample, in the case where G is discrete and 1 < p < ,we find that the module p (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. 2000 MathematicsSubject Classification 46H25, 43A20. |
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Keywords: | group algebras modules homology amenable group Banach algebra |
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