51 citations · 254 across the 64 of their papers we have counts for
75 papers
Constructions and automorphisms of quandles
Valeriy G. Bardakov, Birama Sangare
We prove that if M is an abelian group and X = Alex(M, phi) is a Latin Alexander quandle with id - phi in Aut(M), then Aut(X) is isomorphic to M semidirect C_Aut(M)(phi), Inn(X) is…
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…
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…
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,…
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…