Email this article A categorical approach to the study of derivations in group algebras
- Authors: Arutyunov A.A.1,2
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Affiliations:
- V. A. Trapeznikov Institute of Control Sciences of RAS
- Moscow Institute of Physics and Technology
- Issue: Vol 28, No 142 (2023)
- Pages: 125-136
- Section: Original articles
- URL: https://ogarev-online.ru/2686-9667/article/view/296337
- ID: 296337
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Abstract
We present a review of the results devoted to describing families of operators obeying some inductive identities (e. g. Leibniz’s rule — the case of derivations, Fox derivation, and -derivations) as characters on a suitable groupoid. We first give an implementation of this construction for derivations in group algebras and Fox derivations as characters on an action groupoid. It is also demonstrated how this construction can be realized for derivations on algebras generated by Maltsev semigroups, for the case of derivations with values in finite rings, and for -derivations.
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About the authors
Andronick A. Arutyunov
V. A. Trapeznikov Institute of Control Sciences of RAS; Moscow Institute of Physics and Technology
Author for correspondence.
Email: andronick.arutyunov@gmail.com
ORCID iD: 0000-0002-6878-0993
Candidate of Physics and Mathematics, Senior Researcher; Associate Professor of the Higher Mathematics Department
Russian Federation, 65 Profsoyuznaya St., Moscow 117997, Russian Federation; 9 Inststitutskii Per., Dolgoprudny 141700, Moscow Reg, Russian FederationReferences
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