Garside structure on monoids with quadratic square-free relations
Quantum Algebra
2009-09-28 v1 Group Theory
Abstract
We show the intimate connection between various mathematical notions that are currently under active investigation: a class of Garside monoids, with a "nice" Garside element, certain monoids with quadratic relations, whose monoidal algebra has a Frobenius Koszul dual with regular socle, the monoids of skew-polynomial type (or equivalently, binomial skew-polynomial rings) which were introduced and studied by the author and in 1995 provided a new class of Noetherian Artin-Schelter regular domains, and the square-free set-theoretic solutions of the Yang-Baxter equation. There is a beautiful symmetry in these objects due to their nice combinatorial and algebraic properties.
Keywords
Cite
@article{arxiv.0909.4709,
title = {Garside structure on monoids with quadratic square-free relations},
author = {Tatiana Gateva-Ivanova},
journal= {arXiv preprint arXiv:0909.4709},
year = {2009}
}