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Set-theoretic type solutions of the braid equation

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arxiv 2008.13494 v5 pith:YBARWY66 submitted 2020-08-31 math.RA

Jorge A. Guccione , Juan J. Guccione , Christian Valqui This is my paper · ORCID
classification math.RA
keywords solutionsbraidequationset-theoreticset-theoreticaltypebasicbegin
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abstract

In this paper we begin the study of set-theoretic type solution of the braid equation. Our theory includes set-theoretical solutions as basic examples. We show that the relationships between set-theoretical solutions, q-cycle sets, q-braces, skew-braces, matched pairs of groups and invertible $1$-cocycles remain valid in our setting.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Matched pairs and Yang-Baxter operators

    math.QA 2025-01 accept novelty 7.0 of 10

    A matched pair of actions on a Hopf algebra gives an involutive Yang-Baxter operator exactly when its intrinsic Hopf algebra is braided commutative.

  2. Matched pairs of actions on the Kac-Paljutkin algebra $H_8$

    math.QA 2025-01 conditional novelty 5.0 of 10

    Classification of matched pairs of actions on H8 yields exactly six, two of which give involutive Yang-Baxter operators and are not derived from coquasitriangular structures.

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