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**Homological properties of modules over group algebras.** / Dales, H.G.; Polyakov, M. E.

Research output: Contribution to journal › Journal article › peer-review

Dales, HG & Polyakov, ME 2004, 'Homological properties of modules over group algebras', *Proceedings of the London Mathematical Society*, vol. 89, no. 2, pp. 390-426. https://doi.org/10.1112/S0024611504014686

Dales, H. G., & Polyakov, M. E. (2004). Homological properties of modules over group algebras. *Proceedings of the London Mathematical Society*, *89*(2), 390-426. https://doi.org/10.1112/S0024611504014686

Dales HG, Polyakov ME. Homological properties of modules over group algebras. Proceedings of the London Mathematical Society. 2004 Sep;89(2):390-426. https://doi.org/10.1112/S0024611504014686

@article{8718be456c394361a6f5dbd3a24534a8,

title = "Homological properties of modules over group algebras",

abstract = "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 {\textquoteleft}pseudo-amenable{\textquoteright}, a property very close to that of amenability. ",

author = "H.G. Dales and Polyakov, {M. E.}",

year = "2004",

month = sep,

doi = "10.1112/S0024611504014686",

language = "English",

volume = "89",

pages = "390--426",

journal = "Proceedings of the London Mathematical Society",

issn = "0024-6115",

publisher = "Oxford University Press",

number = "2",

}

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 -