Isotopes of biracks and Zhang twists of algebras

2025/12/03 by Yu, Xiaolan, Zhang, Yanfei
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2512.03384

Abstract

In this paper, we introduce the notion of an ℕ^p-graded birack and construct its isotope. Every involutive ℕ^p-graded birack gives rise to an ℕ^p-graded Yang-Baxter algebra. We study the relation between isotopes of involutive ℕ^p-graded biracks and Zhang twists of ℕ^p-graded Yang-Baxter algebras. As an example, Yang-Baxter algebras determined by distributive solutions are proved to be Zhang twists of polynomial algebras.

Citations

• Set-theoretic solutions of the Yang-Baxter equation, Braces, and\n Symmetric groups
• Set-theoretic solutions of the Yang-Baxter equation, RC-calculus, and Garside germs
• Quadratic algebras, Yang-Baxter equation, and Artin-Schelter regularity
• Quantum spaces associated to multipermutation solutions of level two
• Matched pairs approach to set-theoretic solutions of the Yang-Baxter equation
• Semigroups of I-type

Related

• Twisting of graded quantum groups and solutions to the quantum Yang-Baxter equation
• Combinatorial twists in gl_n Yangians
• Yang-Baxterization of the BH algebra
• Dihedral solutions of the set theoretical Yang-Baxter equation
• Płonka bi-magmas and the set-theoretic Yang--Baxter equation