Garside Groups and Yang–Baxter Equation

By Fabienne Chouraqui. 2009

76 citations recorded by the source corpus.

We establish a one-to-one correspondence between a class of Garside groups admitting a certain presentation and the structure groups of non-degenerate, involutive, and braided set-theoretical solutions of the quantum Yang–Baxter equation. We also characterize indecomposable solutions in terms of Δ-pure Garside groups.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/36d90403c39aa074040e8848fe8f7014d8bb003c

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On Structure Groups of Set-Theoretic Solutions to the Yang–Baxter Equation (2017, background): “In particular, we show that: • G(X,r) is virtually abelian, hence linear, hence residually finite; • the rank of its abelianization is the number kr of its orbits with respect to the actions x 7→ σy(x) and x 7→ τy(x): rk(AbG(X,r)) = kr; • every solution shrinks to an injective one with the same stru”
Quadratic algebras, Yang-Baxter equation, and Artin-Schelter regularity (2010, background): “There is a close relation between Yang-Baxter monoids and a special class of Garside monoids, see [9], and [19].”
Foundations of Garside Theory (2013, result): “Chouraqui in [59]; further results appear in Chouraqui–Godelle [60] and [61].”