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Contemporary Mathematics. Fundamental Directions, 2024, Volume 70, Issue 3, Pages 356–374
DOI: https://doi.org/10.22363/2413-3639-2024-70-3-356-374 (Mi cmfd545) 		 
Triviality of outer derivations in $\ell_p(G)$ for one class of groups

A. A. Arutyunova, A. V. Naianzinb

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Russia
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DOI: https://doi.org/10.22363/2413-3639-2024-70-3-356-374
Abstract: In this paper, we study derivations in group rings completed by various types of norms. The main attention is paid to the class of groups in which conjugations act in a controlled manner in some sense. Using the method of identifying derivations and characters on some category, we obtain an alternative way of proving that for this class of groups all derivations are inner.
Keywords: derivation on algebras, outer derivation, inner derivation, character.
Funding agency Grant number
Russian Science Foundation 22-11-00042
A. A. Arutyunov is supported by a grant from the Russian Science Foundation № 22-11-00042 https://rscf.ru/en/project/22-11-00042/ in the V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences.
English version:
Journal of Mathematical Sciences, 2024, Volume 287, Issue 4, Pages 545–562
DOI: https://doi.org/10.1007/s10958-025-07621-7
Bibliographic databases:
Document Type: Article
UDC: 517.28+512.552
Language: Russian
Citation: A. A. Arutyunov, A. V. Naianzin, “Triviality of outer derivations in $\ell_p(G)$ for one class of groups”, CMFD, 70, no. 3, PFUR, M., 2024, 356–374; Journal of Mathematical Sciences, 287:4 (2024), 545–562
Citation in format AMSBIB
\Bibitem{AruNai24}
\by A.~A.~Arutyunov, A.~V.~Naianzin
\paper Triviality of outer derivations in $\ell_p(G)$ for one class of groups
\serial CMFD
\yr 2024
\vol 70
\issue 3
\pages 356--374
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd545}
\edn{https://elibrary.ru/PFEHJE}
\transl
\jour Journal of Mathematical Sciences
\yr 2024
\vol 287
\issue 4
\pages 545--562
\crossref{https://doi.org/10.1007/s10958-025-07621-7}
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