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This article is cited in 2 scientific papers (total in 2 papers)
On relative homological dimension of group algebras of locally compact groups
M. V. Sheinberg
Abstract:
Let $G$ be a noncompact, locally compact group with an invariant mean, $L_1(G)$ its group algebra, and $I$ the ideal of $L_1(G)$ formed by those functions whose Haar integral is zero.
In this paper it is shown that the (relative) homological dimension of the Banach $L_1(G)$-module $L_1(G)/I$ is infinite. By the same token the (relative) global dimension of the Banach algebra $L_1(G)$ is also infinite. This result is then applied to the study of cohomology groups of a locally compact group with coefficients in Banach $G$-modules.
Received: 14.02.1972
Citation:
M. V. Sheinberg, “On relative homological dimension of group algebras of locally compact groups”, Izv. Akad. Nauk SSSR Ser. Mat., 37:2 (1973), 308–318; Math. USSR-Izv., 7:2 (1973), 307–317
Linking options:
https://www.mathnet.ru/eng/im2248https://doi.org/10.1070/IM1973v007n02ABEH001938 https://www.mathnet.ru/eng/im/v37/i2/p308
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Abstract page: | 229 | Russian version PDF: | 84 | English version PDF: | 9 | References: | 48 | First page: | 1 |
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