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Derivation Algebra in Noncommutative Group Algebras

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Abstract

For a generally infinite noncommutative discrete group G, we study derivation algebras in the group algebra of G in terms of characters on a groupoid associated with the group. We obtain necessary conditions for a character to define a derivation. Using these conditions, we analyze some examples. In particular, we describe a derivation algebra in the case when the group is a nilpotent group of rank 2.

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Acknowledgments

I am grateful to Professor A. S. Mishchenko for his attention to this work.

Funding

This work (except for Subsection 3.3) was supported by a grant of the President of the Russian Federation, project no. MK-2364.2020.1. The study presented in Subsection 3.3 was supported by the Russian Science Foundation under grant 20-11-20131.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701, Russia

    A. A. Arutyunov

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  1. A. A. Arutyunov
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Correspondence to A. A. Arutyunov.

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Russian Text © The Author(s), 2020, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Vol. 308, pp. 28–41.

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Arutyunov, A.A. Derivation Algebra in Noncommutative Group Algebras. Proc. Steklov Inst. Math. 308, 22–34 (2020). https://doi.org/10.1134/S0081543820010022

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