Garside structures on monoids with quadratic square-free relations

DOI10.1007/s10468-010-9220-zzbMath1246.81079arXiv0909.4709OpenAlexW2022935672MaRDI QIDQ434435

Tatiana Gateva-Ivanova

Publication date: 10 July 2012

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.4709

zbMATH Keywords

Yang-Baxter equationquantum groupsquadratic algebrasFrobenius algebrasGarside groupsGarside monoidbinomial skew-polynomial semigroupsquadratic monoids

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Graded rings and modules (associative rings and algebras) (16W50) Quadratic and Koszul algebras (16S37) Yang-Baxter equations (16T25)

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A note on Garside monoids and \({\mathcal{M}} \)-braces ⋮ On some Garsideness properties of structure groups of set-theoretic solutions of the Yang-Baxter equation ⋮ The Yang–Baxter equation and Thompson’s group F ⋮ Quadratic algebras, Yang-Baxter equation, and Artin-Schelter regularity ⋮ Segre products and Segre morphisms in a class of Yang-Baxter algebras ⋮ Finite quotients of groups of I-type. ⋮ Multipermutation solutions of the Yang-Baxter equation ⋮ A combinatorial approach to noninvolutive set-theoretic solutions of the Yang-Baxter equation ⋮ Folding of set-theoretical solutions of the Yang-Baxter equation. ⋮ An algorithmic construction of group automorphisms and the quantum Yang-Baxter equation ⋮ Finitely generated algebras defined by homogeneous quadratic monomial relations and their underlying monoids. ⋮ Set-theoretic solutions of the Yang-Baxter equation, RC-calculus, and Garside germs. ⋮ The matched product of set-theoretical solutions of the Yang-Baxter equation

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