2-dimensional self-distributive non-counital bialgebras and knot invariants
Quantum Algebra
2025-02-25 v1 Group Theory
Abstract
In the preprint of V. Bardakov, T. Kozlovskaya, D. Talalaev (Self-distributive bialgebras, arXiv:2501.19152) it was formulated a problem of classification of self-distributive bialgebras and was given classification of two-dimensional counital self-distributive bialgebras. In this paper, we consider non-counital case. We find all 2-dimensional algebras of this type. In constructed algebras we study the question of finding quandles for constructing knot invariants. This activity is part of the overall program for the linearization of the concepts of rack and quandle and the development of the representations theory of these structures.
Keywords
Cite
@article{arxiv.2502.16875,
title = {2-dimensional self-distributive non-counital bialgebras and knot invariants},
author = {Valeriy G. Bardakov and Tatiana A. Kozlovskaya and Alexander S. Panasenko and Dmitry V. Talalaev},
journal= {arXiv preprint arXiv:2502.16875},
year = {2025}
}