Hecke algebras for set-theoretical solutions to the Yang–Baxter equation

In this paper, we define a notion of Hecke algebras for structure groups of set-theoretical solutions to the Yang–Baxter equation. As a comparison to the Iwahori–Hecke algebras of Artin–Tits groups of spherical type, we show that this construction has the expected classical properties. We also highlight how these constructions, and more generally Dehornoy’s “Coxeter-like” group, slightly differ from the classical Artin–Tits case. Finally, we study a particular case which relates to torus knot groups and complex reflection groups.