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

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-à 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

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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

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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