Non-unitary set-theoretical solutions to the Quantum Yang-Baxter Equation

Abstract

We develop a theory of non-unitary set-theoretical solutions to the Quantum Yang-Baxter equation. Our results generalize those obtained by Etingof, Schedler and the author. We remark that some of our constructions are similar to constructions obtained by Lu, Yan and Zhu.

AMS-LaTeX v1.2, 19 pages, no figures, corrected small mistakes in the proofs of Lemma 3 and Theorem 2.8

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• Yang-Baxter maps: dynamical point of view
• Nichols algebras of group type with many quadratic relations
• Cohomology and extensions of braces
• Enumeration of set-theoretic solutions to the Yang-Baxter equation
• Combinatorial solutions to the reflection equation
• Yang-Baxter operators in symmetric categories
• Retractability of solutions to the Yang-Baxter equation and $p$-nilpotency of skew braces
• Skew braces of size $p^{2}q$ I: abelian type
• The structure skew brace associated with a finite non-degenerate solution of the Yang-Baxter equation is finitely presented