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Right groups and the set-theoretic Yang-Baxter equation

· 2026 · math.GR · arXiv 2605.25660

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abstract

In this paper, we provide techniques to obtain left non-degenerate set-theoretic solutions of the Yang-Baxter equation, drawing on the class of right groups. To this end, we introduce the new algebraic structures of left $RG$-semibraces, which include left (cancellative) semibraces as a proper subclass.

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Right groups, left quasigroups, and right heaps

math.GR · 2026-06-08 · unverdicted · novelty 5.0

Introduces right heaps and related structures from right groups and left quasigroups as a framework for left non-degenerate Yang-Baxter solutions.

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  • Right groups, left quasigroups, and right heaps math.GR · 2026-06-08 · unverdicted · none · ref 1 · internal anchor

    Introduces right heaps and related structures from right groups and left quasigroups as a framework for left non-degenerate Yang-Baxter solutions.