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Mathematics of the USSR-Izvestiya, 1973, Volume 7, Issue 2, Pages 307–317
DOI: https://doi.org/10.1070/IM1973v007n02ABEH001938
(Mi im2248)
 

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
References:
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
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1973, Volume 37, Issue 2, Pages 308–318
Bibliographic databases:
UDC: 513.88
MSC: Primary 22D15, 18G20, 18G25; Secondary 18H10
Language: English
Original paper language: Russian
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/im2248}
\mathscinet{http://mathscinet.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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  • https://doi.org/10.1070/IM1973v007n02ABEH001938
  • https://www.mathnet.ru/eng/im/v37/i2/p308
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:229
    Russian version PDF:84
    English version PDF:9
    References:48
    First page:1
     
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