Abstract
Let be a noncompact, locally compact group with an invariant mean, its group algebra, and the ideal of formed by those functions whose Haar integral is zero. In this paper it is shown that the (relative) homological dimension of the Banach -module is infinite. By the same token the (relative) global dimension of the Banach algebra is also infinite. This result is then applied to the study of cohomology groups of a locally compact group with coefficients in Banach -modules.
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