Geodesic
A categorical approach to the study of derivations in group algebras
Vestnik rossijskih universitetov. Matematika, Tome 28 (2023) no. 142, pp. 125-136

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $(\sigma,\tau)$-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 $(\sigma,\tau)-$derivations.
Keywords: derivation, Fox derivative, operator algebra, identity
Mots-clés : groupoid. 
@article{VTAMU_2023_28_142_a2,
     author = {A. A. Arutyunov},
     title = {A categorical approach to the study of derivations in group algebras},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {125--136},
     publisher = {mathdoc},
     volume = {28},
     number = {142},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2023_28_142_a2/}
}
TY  - JOUR
AU  - A. A. Arutyunov
TI  - A categorical approach to the study of derivations in group algebras
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2023
SP  - 125
EP  - 136
VL  - 28
IS  - 142
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2023_28_142_a2/
LA  - ru
ID  - VTAMU_2023_28_142_a2
ER  - 
%0 Journal Article
%A A. A. Arutyunov
%T A categorical approach to the study of derivations in group algebras
%J Vestnik rossijskih universitetov. Matematika
%D 2023
%P 125-136
%V 28
%N 142
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VTAMU_2023_28_142_a2/
%G ru
%F VTAMU_2023_28_142_a2
A. A. Arutyunov. A categorical approach to the study of derivations in group algebras. Vestnik rossijskih universitetov. Matematika, Tome 28 (2023) no. 142, pp. 125-136. http://geodesic.mathdoc.fr/item/VTAMU_2023_28_142_a2/