English

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 SS with quadratic relations, whose monoidal algebra A=k[S]A= k[S] has a Frobenius Koszul dual A!A^{!} 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}
}
R2 v1 2026-06-21T13:50:36.371Z