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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 2, Pages 308–318 (Mi izv2248)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:2, 307–317

Bibliographic databases:

UDC: 513.88
MSC: Primary 22D15, 18G20, 18G25; Secondary 18H10
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

Citation in format AMSBIB
\Bibitem{She73}
\by M.~V.~Sheinberg
\paper On relative homological dimension of group algebras of locally compact groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 2
\pages 308--318
\mathnet{http://mi.mathnet.ru/izv2248}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=328623}
\zmath{https://zbmath.org/?q=an:0259.22011}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 2
\pages 307--317
\crossref{https://doi.org/10.1070/IM1973v007n02ABEH001938}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. Yu. Aristov, “The global dimension theorem for non-unital and certain other separable $C^*$-algebras”, Sb. Math., 186:9 (1995), 1223–1239  mathnet  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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