Self-distributive algebras and bialgebras

Self-distributive algebras and bialgebras Full article

Journal

Theoretical and Mathematical Physics (Russian Federation)
ISSN: 0040-5779 , E-ISSN: 1573-9333

Output data

Year: 2025, Volume: 224, Number: 1, Pages: 1103-1118 Pages count : 16 DOI: 10.1134/S0040577925070013

Tags

algebra, coalgebra, bialgebra, rack, quandle, rack algebra, rack bialgebra, self-distributivity, Yang–Baxter equation

Authors

Bardakov V.G. ^1,2,3 , Kozlovskaya T.A. ³ , Talalaev D.V. ^4,5

Affiliations

1	Sobolev Institute of Mathematics, Novosibirsk, Russia
2	Novosibirsk State Agrarian University, Novosibirsk, Russia
3	Regional Scientific and Educational Mathematical Center of Tomsk State University, Tomsk, Russia
4	Lomonosov Moscow State University, Moscow, Russia
5	Center of Integrable Systems, Demidov Yaroslavl State University, Yaroslavl, Russia

Funding (3)

1	Russian Science Foundation	20-71-10110
2	Министерство науки и высшего образования РФ	075-02-2025-1728/2
3	Министерство науки и высшего образования РФ	075-02-2025-1636

We study self-distributive algebraic structures: algebras, bialgebras, additional structures on them, relations of these structures with Hopf algebras, Lie algebras, Leibnitz algebras, etc. The basic example of such structures is given by rack and quandle bialgebras. But we go further to the general coassociative comultiplication. The principal motivation for this work is the development of linear algebra related to the notion of a quandle in analogy with the ubiquitous role of group algebras in the category of groups with possible applications to the theory of knot invariants. We describe self-distributive algebras and show that some quandle algebras and some Novikov algebras are self-distributive. We also give a full classification of counital self-distributive bialgebras in dimension 2 over C.

Bardakov V.G. , Kozlovskaya T.A. , Talalaev D.V.
Self-distributive algebras and bialgebras
Theoretical and Mathematical Physics (Russian Federation). 2025. V.224. N1. P.1103-1118. DOI: 10.1134/S0040577925070013 WOS Scopus РИНЦ OpenAlex

Bardakov V.G. , Kozlovskaya T.A. , Talalaev D.V.
Самодистрибутивные алгебры и биалгебры
Теоретическая и математическая физика. 2025. Т.224. №1. С.3-21. DOI: 10.4213/tmf10900 РИНЦ OpenAlex

Submitted:	Jan 21, 2025
Accepted:	Apr 6, 2025
Published print:	Jul 25, 2025
Published online:	Jul 25, 2025

Web of science:	WOS:001536229400005
Scopus:	2-s2.0-105011771558
Elibrary:	82684524
OpenAlex:	W4412718167

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