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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, Number 12, Pages 74–81
DOI: https://doi.org/10.26907/0021-3446-2020-12-74-81 (Mi ivm9636) 		 
Brief communications

Combinatorial description of derivations in group algebras

A. A. Arutyunovab

a Moscow Institute of Physics and Technologies, 9 Institutskiy Ln., Dolgoprudny, 141701 Russia
b V.A. Trapeznikov Institute of Control Sciences of RAS, 65 Profsoyuznaya str., Moscow 117997, Russia
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DOI: https://doi.org/10.26907/0021-3446-2020-12-74-81
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 differentiations of group algebras with the theory of ends of groups and in particular 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.
Keywords: group algebra, Stallings theorem, derivations, ends of group.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation МК-2364.2020.1
075-00337-20-03, проект № 0714-2020-0005
Received: 24.09.2020
Revised: 24.09.2020
Accepted: 01.10.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2020, Volume 64, Issue 12, Pages 67–73
DOI: https://doi.org/10.3103/S1066369X20120075
Bibliographic databases:
Document Type: Article
UDC: 512.552: 512.554
Language: Russian
Citation: A. A. Arutyunov, “Combinatorial description of derivations in group algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 12, 74–81; Russian Math. (Iz. VUZ), 64:12 (2020), 67–73
Citation in format AMSBIB
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\paper Combinatorial description of derivations in group algebras
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\pages 74--81
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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