51 citations
3 papers
math.QA2022★ 5 cited
Extensions of Yang-Baxter sets
Valeriy G. Bardakov, Dmitry V. Talalaev
The paper extends the notion of braided set and its close relative - the Yang-Baxter set - to the category of vector spaces and explore structure aspects of such a notion as morphi…
math.GR2021★ 25 cited
Rota-Baxter operators on groups
Valeriy G. Bardakov, Vsevolod Gubarev
Theory of Rota-Baxter operators on rings and algebras has been developed since 1960. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] have defined the notion of Rota-Baxter o…
math.GR2021★ 51 cited
Rota-Baxter groups, skew left braces, and the Yang-Baxter equation
Valeriy G. Bardakov, Vsevolod Gubarev
Braces were introduced by W. Rump in 2006 as an algebraic system related to the quantum Yang-Baxter equation. In 2017, L. Guarnieri and L. Vendramin defined for the same purposes a…