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Combinatorial Description of Derivations in Group Algebras

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Abstract

The work is devoted to the study of derivations in group algebras using the results of combinatorial group theory. A survey of old results is given, describing derivations in group algebras as characters on an adjoint action groupoid. In this paper, new assertions are presented that make it possible to connect derivations of group algebras with the theory of ends of groups and in particular the Stallings theorem. A homological interpretation of the results obtained is also given. We also construct a generalization of the proposed construction for the case of modules over a group ring.

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Funding

The work (except for Theorem 8) is performed under the grant of the President of the Russian Federation (project MK-2364.2020.1). Theorem 8 is obtained under financial support of the Ministry of Science and Higher Education of the Russian Federation (state assignment 075-00337-20-03, project no. 0714-2020-0005).

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Authors and Affiliations

  1. Moscow Institute of Physics and Technologies, 9 Institutskiy ln., 141701, Dolgoprudny, Russia

    A. A. Arutyunov

  2. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya str., 117997, Moscow, Russia

    A. A. Arutyunov

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

Additional information

Communicated by V. P. Maksimov.

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 12, pp. 74–81.

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Arutyunov, A.A. Combinatorial Description of Derivations in Group Algebras. Russ Math. 64, 67–73 (2020). https://doi.org/10.3103/S1066369X20120075

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