Skew lattices and set-theoretic solutions of the Yang-Baxter equation
Abstract
In this paper we discuss and characterize several set-theoretic solutions of the Yang-Baxter equation obtained using skew lattices, an algebraic structure that has not yet been related to the Yang-Baxter equation. Such solutions are degenerate in general, and thus different from solutions obtained from braces and other algebraic structures. Our main result concerns a description of a set-theoretic solution of the Yang-Baxter equation, obtained from an arbitrary skew lattice. We also provide a construction of a cancellative and distributive skew lattice on a given family of pairwise disjoint sets.
Keywords
Cite
@article{arxiv.1907.03440,
title = {Skew lattices and set-theoretic solutions of the Yang-Baxter equation},
author = {Karin Cvetko-Vah and Charlotte Verwimp},
journal= {arXiv preprint arXiv:1907.03440},
year = {2020}
}
Comments
The definition of a simply cancellative skew lattice on page 25 should correctly be stated as: $x \lor z\lor x = y\lor z \lor y, x \land z \land x =y \land z \land y \Longrightarrow x = y.$ All results in the paper were obtained using the correct definition