Self-distributive algebras and bialgebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912375176691712 |
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| author | Bardakov, Valeriy G. Kozlovskaya, Tatiana A. Talalaev, Dmitry V. |
| author_facet | Bardakov, Valeriy G. Kozlovskaya, Tatiana A. Talalaev, Dmitry V. |
| contents | This article is devoted to the study of 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 are rack- and quandle bialgebras. But we go further - to the general coassociative comultiplication. The principal motivation for this work is the development of the linear algebra related with a notion of a quandle in analogy with the ubiquitous role of group algebras in the category of groups with perspective applications to the theory of knot invariants. We give description of self-distributive algebras and show that some quandle algebras and some Novikov algebras are self-distributive. Also, we give a full classification of counital self-distributive bialgebras in dimension 2 over C. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-distributive algebras and bialgebras Bardakov, Valeriy G. Kozlovskaya, Tatiana A. Talalaev, Dmitry V. Rings and Algebras This article is devoted to the study of 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 are rack- and quandle bialgebras. But we go further - to the general coassociative comultiplication. The principal motivation for this work is the development of the linear algebra related with a notion of a quandle in analogy with the ubiquitous role of group algebras in the category of groups with perspective applications to the theory of knot invariants. We give description of self-distributive algebras and show that some quandle algebras and some Novikov algebras are self-distributive. Also, we give a full classification of counital self-distributive bialgebras in dimension 2 over C. |
| title | Self-distributive algebras and bialgebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2501.19152 |