n-valued quandles and associated bialgebras
Group Theory
2023-12-20 v1 Mathematical Physics
math.MP
Abstract
The principal aim of this article is to introduce and study n-valued quandles and n-corack bialgebras. We elaborate the basic methods of this theory, reproduce the coset construction known in the theory of n-valued groups. We also consider a construction of n-valued quandles using n-multi-quandles. In contrast to the case of n-valued groups this construction turns out to be quite rich in algebraic and topological applications. An important part of the work is the study of the properties of n-corack bialgebras those role is analogous to the group bialgebra.
Cite
@article{arxiv.2312.12007,
title = {n-valued quandles and associated bialgebras},
author = {Valeriy G. Bardakov and Tatyana A. Kozlovskaya and Dmitry V. Talalaev},
journal= {arXiv preprint arXiv:2312.12007},
year = {2023}
}
Comments
22 pages