Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Homological properties of modules over group algebras
AU - Dales, H.G.
AU - Polyakov, M. E.
PY - 2004/9
Y1 - 2004/9
N2 - 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.
AB - 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.
U2 - 10.1112/S0024611504014686
DO - 10.1112/S0024611504014686
M3 - Journal article
VL - 89
SP - 390
EP - 426
JO - Proceedings of the London Mathematical Society
JF - Proceedings of the London Mathematical Society
SN - 0024-6115
IS - 2
ER -