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 more general notion of a skew left brace. In 2020, L. Guo, H. Lang and Y. Sheng gave a definition of what is a Rota—Baxter operator on a group. We connect these two notions as follows. It is shown that every Rota—Baxter group gives rise to a skew left brace. Moreover, every skew left brace can be injectively embedded into a Rota—Baxter group. When the additive group of a skew left brace is complete, then this brace is induced by a Rota—Baxter group. We interpret some notions of the theory of skew left braces in terms of Rota—Baxter operators.
Предметные области OECD FOS+WOS
- 1.01 МАТЕМАТИКА