Abstract:
The work is devoted to a survey of known results related to the study of derivations in group algebras, bimodules and other algebraic structures, as well as to various generalizations and variations of this problem. A review of results on derivations in L1(G) algebras, in von Neumann algebras, and in Banach bimodules is given. Algebraic problems are discussed, in particular, derivations in groups, (σ,τ)-derivations, and the Fox calculus. A review of some results related to the application to pseudodifferential operators and the construction of the symbolic calculus is also given. In conclusion, some results related to the description of derivations as characters on the groupoid of the adjoint action are described. Some applications are also described: to coding theory, the theory of ends of metric spaces, and rough geometry.
Keywords:
derivations, operator algebras, group algebras, (σ,τ)-derivations, von Neumann algebras, Banach bimodules.
The study was supported by the Ministry of Science and Higher Education of the Russian Federation (State Assignment No. 075-00337-20-03), Project No. 0714-2020-0005.
Citation:
A. A. Arutyunov, “On derivations in group algebras and other algebraic structures”, Russian Universities Reports. Mathematics, 27:140 (2022), 305–317
\Bibitem{Aru22}
\by A.~A.~Arutyunov
\paper On derivations in group algebras and other algebraic structures
\jour Russian Universities Reports. Mathematics
\yr 2022
\vol 27
\issue 140
\pages 305--317
\mathnet{http://mi.mathnet.ru/vtamu267}
\crossref{https://doi.org/10.20310/2686-9667-2022-27-140-305-317}
Linking options:
https://www.mathnet.ru/eng/vtamu267
https://www.mathnet.ru/eng/vtamu/v27/i140/p305
This publication is cited in the following 2 articles:
A. A. Arutyunov, “Kategornyi podkhod k issledovaniyu differentsirovanii v gruppovykh algebrakh”, Vestnik rossiiskikh universitetov. Matematika, 28:142 (2023), 125–136
A. A. Arutyunov, “Differential Calculi in Group Algebras and Group Ends”, Math. Notes, 114:2 (2023), 133–146
Citation in format AMSBIB
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