Near braces and p-deformed braided groups

Abstract

Motivated by recent findings on the derivation of parametric non-involutive solutions of the Yang-Baxter equation we reconstruct the underlying algebraic structures, called near braces. Using the notion of the near braces we produce new multi-parametric, non-degenerate, non-involutive solutions of the set-theoretic Yang-Baxter equation. These solutions are generalisations of the known ones coming from braces and skew braces. Bijective maps associated to the inverse solutions are also constructed. Furthermore, we introduce the generalized notion of p-deformed braided groups and p-braidings and we show that every p-braiding is a solution of the braid equation. We also show that certain multi-parametric maps within the near braces provide special cases of p-braidings.

arXiv comment17 pages, LaTex. Minor modifications and two new examples added. arXiv admin note: text overlap with arXiv:2204.11580

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Cited by in corpus (3)

• Quandles as pre-Lie skew braces, set-theoretic Hopf algebras & universal R-matrices
• Self-distributive structures, braces & the Yang-Baxter equation
• Algebraic structures in set-theoretic Yang-Baxter & reflection equations