Quasi racks, quasi bijective and quasi non-degenerate set-theoretic solutions of the Yang-Baxter equation

2025/12/03 by Mazzotta, Marzia, Stefanelli, Paola, Wiertel, Magdalena
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2512.04215

Abstract

This work initiates a systematic study of the class of quasi bijective and quasi non-degenerate solutions to the set-theoretic Yang-Baxter equation. The motivation stems from the observation that solutions that arise from dual weak braces belong to this class. The notions of quasi rack and derived solution are introduced and examined, extending the classical definitions. Additionally, a family of quasi left non-degenerate solutions is described in terms of quasi racks and g-twists, analogous to the left non-degenerate case. Furthermore, we completely characterize a class of quasi racks expressible in terms of Plonka sum of racks.

Citations

• Diagonals of solutions of the Yang-Baxter equation
• Idempotent solutions of the Yang-Baxter equation and twisted group\n division
• Applications of self-distributivity to Yang-Baxter operators and their cohomology

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