Geodesic
Differentional calculuses in group algebras
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2023), pp. 89-94.

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In this paper we present results devoted to the description of families of operators obeying some inductive identities (e.g. the Leibniz rule, the case of differentiations, Fox differentiations) as characters on a suitable groupoid. In the first place, we give an implementation of this construction for differentiations in group algebras and Fox differentiations as characters on an action groupoid.
Keywords: derivations, Fox derivative, operator algebra, identity
Mots-clés : groupoid. 
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A. A. Arutyunov. Differentional calculuses in group algebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2023), pp. 89-94. http://geodesic.mathdoc.fr/item/IVM_2023_6_a7/

[1] Matiyasevich Yu. V., “Diofantovost perechislimykh mnozhestv”, DAN SSSR, 191:2 (1970), 279–282 | Zbl

[2] Kharlampovich O., Myasnikov A., “Equations in Algebras”, Int. J. Algebra and Comput., 28:08 (2018), 1517–1533 | DOI | MR | Zbl

[3] Perov A. I., Kostrub I. D., “Differentsialnye uravneniya v banakhovykh algebrakh”, Dokl. RAN. Matem., inform., prots. upr., 491 (2020), 73–77 | DOI | Zbl

[4] Perov A. I., Kostrub I. D., “O differentsialnykh uravneniyakh v banakhovykh algebrakh”, Vestn. rossiisk. un-tov. Matem., 25:132 (2020), 410–421 | Zbl

[5] Parshin A. N., “O koltse formalnykh psevdodifferentsialnykh operatorov”, Algebra. Topologiya. Diff. uravneniya i ikh prilozh., Tr. MIAN, 224, Nauka, M., 1999, 291–305

[6] Arutyunov A., “On a Pseudodifferentional Calculation in Group Algebras”, Adv. Systems Sci. and Appl., 22:4 (2022), 11–18 | MR

[7] Arutyunov A. A., Mischenko A. S., Shtern A. I., “Derivatsii gruppovykh algebr”, Fundament. i prikl. matem., 21:6 (2016), 65–78

[8] Arutyunov A. A., Mischenko A. S., “Gladkaya versiya problemy Dzhonsona o derivatsiyakh gruppovykh algebr”, Matem. sb., 210:6 (2019), 3–29 | DOI | MR | Zbl

[9] Arutyunov A. A., Alekseev A. V., “Cohomology of n-categories and derivations in group algebras”, Topology and Appl., 275 (2020) | DOI | MR

[10] Burghelea D., “The cyclic homology of the group rings”, Coment. Math. Helv., 60:1 (1985), 354–365 | DOI | MR | Zbl

[11] Mischenko A. S., “Derivations of Group Algebras and Hochschild Cohomology”, Diff. Equat. Manifolds and Math. Phys., 2022, 263–272 | MR

[12] Creedon L., Hughes K., “Derivations on Group Algebras with Coding Theory Applications”, Finite Fields and Their Appl., 56 (2019), 247–265 | DOI | MR | Zbl

[13] Crowell R. H., Fox R. H., Introduction to Knot Theory, Springer-Verlag, Berlin, 1963 | MR

[14] Fox R. H., “Free Differential Calculus I”, Ann. Math., 57:3 (1953), 547–560 | DOI | MR