Homological properties of modules over group algebras

• Autores: H. G. Dales, M. E. Polyakov
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 89, Nº 2, 2004, págs. 390-426
• Idioma: inglés
• DOI: 10.1112/s0024611504014686
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• Resumen

  • Let $G$ be a locally compact group, and let $L^1 (G)$ be the Banach algebra which is the group algebra of $G$. We consider a variety of Banach left $L^1 (G)$ -modules over $L^1 (G)$ , 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 $1 < p < \infty$, we find that the module $\ell^p (G)$ 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.