Solutions of the Yang-Baxter equation associated to skew left braces, with applications to racks

David Bachiller

    Research output: Contribution to journalArticleResearchpeer-review

    15 Citations (Scopus)

    Abstract

    © 2018 World Scientific Publishing Company. Given a skew left brace B, a method is given to construct all the non-degenerate set-theoretic solutions (X,r) of the Yang-Baxter equation such that the associated permutation group (X,r) is isomorphic, as a skew left brace, to B. This method depends entirely on the brace structure of B. We then adapt this method to show how to construct solutions with additional properties, like square-free, involutive or irretractable solutions. Using this result, it is even possible to recover racks from their permutation group.
    Original languageEnglish
    Article number1850055
    JournalJournal of Knot Theory and its Ramifications
    Volume27
    Issue number8
    DOIs
    Publication statusPublished - 1 Jul 2018

    Keywords

    • Hopf-Galois extensions
    • Yang-Baxter equation
    • quandle
    • rack
    • set-theoretic solution
    • skew left brace

    Fingerprint

    Dive into the research topics of 'Solutions of the Yang-Baxter equation associated to skew left braces, with applications to racks'. Together they form a unique fingerprint.

    Cite this