String Theory Journal Club

I will present several examples of set-theoretical solutions to the Yang-Baxter and entwining Yang-Baxter equations. I will first describe how such (parametric) solutions to the Yang-Baxter equation, called Yang-Baxter maps, can be obtained from refactorisation problems of Darboux matrices associated to certain integrable PDEs of soliton theory. Then I will present a generalisation of such maps over Grassmann algebras and I will discuss some of their integrability properties (Lax representation, invariants) in this non-commutative setting.