9 papers
Multi-virtual braid groups
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Komal Negi +1
L. Kauffman (2024) introduced multi-virtual and symmetric multi-virtual braid groups, which are generalizations of the virtual braid group. We introduce multi-virtual pure and mult…
Idempotents and Powers of Ideals in Quandle Rings
Valeriy Bardakov, Mohamed Elhamdadi
This article addresses two central problems in the theory of quandle rings. First, motivated by Conjecture 3.10 in Internat. J. Math. 34 (2023), no. 3, Paper No. 2350011: for a sem…
Yang-Baxter Equation and Related Algebraic Structures
Valeriy Bardakov, Mohamed Elhamdadi, Mahender Singh
In the 1990s, Drinfel'd proposed the study of set-theoretical solutions to the quantum Yang-Baxter equation, initiating a line of research that has since garnered substantial atten…
Cayley graphs and their growth functions for multivalued groups
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Matvei N. Zonov
We define the Cayley graph and its growth function for multivalued groups. We prove that if we change a finite set of generators of multivalued group, or change the starting point,…
Self-distributive algebras and bialgebras
Valeriy G. Bardakov, Tatiana A. Kozlovskaya, Dmitry V. Talalaev
This article is devoted to the study of self-distributive algebraic structures: algebras, bialgebras; additional structures on them, relations of these structures with Hopf algebra…
Invariants of Handlebody-Links and Spatial Graphs
V. G. Bardakov, D. A. Fedoseev
A family of quandles is an algebraic construction which was proposed by A. Ishii, M. Iwakiri, Y. Jang, K. Oshiro in 2013. The axioms of these algebraic systems were motivated b…