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Self-distributive algebras and bialgebras Научная публикация

Журнал

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

Вых. Данные

Год: 2025, Том: 224, Номер: 1, Страницы: 1103-1118 Страниц : 16 DOI: 10.1134/S0040577925070013

Ключевые слова

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

Авторы

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

Организации

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

Информация о финансировании (3)

1	Российский научный фонд	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

Поступила в редакцию:	21 янв. 2025 г.
Принята к публикации:	6 апр. 2025 г.
Опубликована в печати:	25 июл. 2025 г.
Опубликована online:	25 июл. 2025 г.

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

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