Home > Research > Publications & Outputs > Homological properties of modules over group al...
View graph of relations

Homological properties of modules over group algebras

Research output: Contribution to journalJournal article

Published

Standard

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

In: Proceedings of the London Mathematical Society, Vol. 89, No. 2, 09.2004, p. 390-426.

Research output: Contribution to journalJournal article

Harvard

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

APA

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

Vancouver

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

Author

Dales, H.G. ; Polyakov, M. E. / Homological properties of modules over group algebras. In: Proceedings of the London Mathematical Society. 2004 ; Vol. 89, No. 2. pp. 390-426.

Bibtex

@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 ‘pseudo-amenable’, a property very close to that of amenability.",
author = "H.G. Dales and Polyakov, {M. E.}",
year = "2004",
month = "9",
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",

}

RIS

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 -