A new family of set-theoretic solutions of the Yang–Baxter equation

A new family of set-theoretic solutions of the Yang–Baxter equation

A new family of non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation is constructed. Two subfamilies, consisting of irretractable square-free solutions, are new counterexamples to Gateva-Ivanova's Strong Conjecture [7]. They are in addition to those obtained by Vendrami...

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Bibliographic Details
Published in:Communications in algebra Vol. 46; no. 4; pp. 1622 - 1629
Main Authors: Castelli, M., Catino, F., Pinto, G.
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis Ltd 03-04-2018
Online Access:Get full text
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Summary:A new family of non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation is constructed. Two subfamilies, consisting of irretractable square-free solutions, are new counterexamples to Gateva-Ivanova's Strong Conjecture [7]. They are in addition to those obtained by Vendramin [15] and [1].
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2017.1350700