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Mat. Sb., 2019, Volume 210, Number 6, Pages 3–29 (Mi msb9119)  

This article is cited in 2 scientific papers (total in 2 papers)

A smooth version of Johnson's problem on derivations of group algebras

A. A. Arutyunova, A. S. Mishchenkob

a Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We give a description of the algebra of outer derivations of the group algebra of a finitely presented discrete group in terms of the Cayley complex of the groupoid of the adjoint action of the group. This problem is a smooth version of Johnson's problem on derivations of a group algebra. We show that the algebra of outer derivations is isomorphic to the one-dimensional compactly supported cohomology group of the Cayley complex over the field of complex numbers.
Bibliography: 34 titles.

Keywords: derivations, group algebras, groupoids, Cayley complexes, Hochschild cohomology.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00398-а
This research was supported by the Russian Foundation for Basic Research (grant no. 18-01-00398-a).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm9119

Full text: PDF file (937 kB)
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English version:
Sbornik: Mathematics, 2019, 210:6, 756–782

Bibliographic databases:

UDC: 512.552.16+515.146.3
MSC: Primary 16W25; Secondary 16E40, 16S34, 20C05, 20C07
Received: 03.04.2018 and 06.12.2018

Citation: A. A. Arutyunov, A. S. Mishchenko, “A smooth version of Johnson's problem on derivations of group algebras”, Mat. Sb., 210:6 (2019), 3–29; Sb. Math., 210:6 (2019), 756–782

Citation in format AMSBIB
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\paper A~smooth version of Johnson's problem on derivations of group algebras
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\pages 3--29
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\jour Sb. Math.
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\pages 756--782
\crossref{https://doi.org/10.1070/SM9119}
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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. A. A. Arutyunov, “Derivation Algebra in Noncommutative Group Algebras”, Proc. Steklov Inst. Math., 308 (2020), 22–34  mathnet  crossref  crossref  isi  elib
    2. A. V. Alekseev, A. A. Arutyunov, “Derivations in semigroup algebras”, Eurasian Math. J., 11:2 (2020), 9–18  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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