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Sbornik: Mathematics, 2019, Volume 210, Issue 6, Pages 756–782
DOI: https://doi.org/10.1070/SM9119 (Mi sm9119) 		 
This article is cited in 23 scientific papers (total in 23 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
English version PDF (791 kB) Citations (23)
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DOI: https://doi.org/10.1070/SM9119
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).
Received: 03.04.2018 and 06.12.2018
Russian version:
Matematicheskii Sbornik, 2019, Volume 210, Number 6, Pages 3–29
DOI: https://doi.org/10.4213/sm9119
Bibliographic databases:
Document Type: Article
UDC: 512.552.16+515.146.3
MSC: Primary 16W25; Secondary 16E40, 16S34, 20C05, 20C07
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 23 articles:
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