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Indecomposable Involutive Set-Theoretic Solutions of the Yang–Baxter Equation and Orthogonal Dynamical Extensions of Cycle Sets

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Abstract

Employing the algebraic structure of the left brace and the dynamical extensions of cycle sets, we investigate a class of indecomposable involutive set-theoretic solutions of the Yang–Baxter equation having specific imprimitivity blocks. Moreover, we study one-generator left braces of multipermutation level 2.

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Authors and Affiliations

  1. Department of Mathematics and Physics “Ennio De Giorgi”, University of Salento, Via per Arnesano, 73100, Lecce (LE), Italy

    Marco Castelli, Francesco Catino & Paola Stefanelli

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  1. Marco Castelli
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  2. Francesco Catino
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  3. Paola Stefanelli
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Correspondence to Marco Castelli.

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This work was partially supported by the Department of Mathematics and Physics “Ennio De Giorgi”— University of Salento. The authors are members of GNSAGA (INdAM)

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Castelli, M., Catino, F. & Stefanelli, P. Indecomposable Involutive Set-Theoretic Solutions of the Yang–Baxter Equation and Orthogonal Dynamical Extensions of Cycle Sets. Mediterr. J. Math. 18, 246 (2021). https://doi.org/10.1007/s00009-021-01912-4

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  • DOI: https://doi.org/10.1007/s00009-021-01912-4

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