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Matematicheskie Zametki, 2023, Volume 114, Issue 2, Pages 163–180
DOI: https://doi.org/10.4213/mzm13873 (Mi mzm13873) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Differential Calculi in Group Algebras and Group Ends

A. A. Arutyunovab

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
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DOI: https://doi.org/10.4213/mzm13873
Abstract: Graphs generalizing Cayley graphs and arising from various actions of groups on themselves are studied. A relationship between such graphs and subalgebras of operators in a group ring is established, which permits one to obtain a formula for the number of ends of such graphs in terms of the dimensions of appropriate character spaces. Examples of group actions and the corresponding graphs are constructed. In particular, under the action by conjugation, the corresponding algebra turns out to be an algebra of derivations. The proposed construction is generalized to Fox derivatives.
Keywords: group action, graph end, coarse geometry, derivation, Fox derivation.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0714-2020-0005
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (government order no. 075-00337-20-03, grant no. 0714-2020-0005).
Received: 09.01.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 2, Pages 133–146
DOI: https://doi.org/10.1134/S0001434623070155
Bibliographic databases:
Document Type: Article
UDC: 512.552.7+519.173.5
MSC: 05E16; 16W25
Language: Russian
Citation: A. A. Arutyunov, “Differential Calculi in Group Algebras and Group Ends”, Mat. Zametki, 114:2 (2023), 163–180; Math. Notes, 114:2 (2023), 133–146
Citation in format AMSBIB
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\by A.~A.~Arutyunov
\paper Differential Calculi in Group Algebras and Group Ends
\jour Mat. Zametki
\yr 2023
\vol 114
\issue 2
\pages 163--180
\mathnet{http://mi.mathnet.ru/mzm13873}
\crossref{https://doi.org/10.4213/mzm13873}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=587399}
\transl
\jour Math. Notes
\yr 2023
\vol 114
\issue 2
\pages 133--146
\crossref{https://doi.org/10.1134/S0001434623070155}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85168583401}
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    • This publication is cited in the following 1 articles:
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