Dynamical Yang-Baxter maps and Hopf algebroids associated with s-sets

Abstract

An s-set is an algebraic generalization of the regular s-manifold introduced by Kowalski, one of the generalized symmetric spaces in differential geometry. We prove that suitable s-sets give birth to dynamical Yang-Baxter maps, set-theoretic solutions to a version of the quantum dynamical Yang-Baxter equation. As an application, Hopf algebroids and rigid tensor categories are constructed by means of these dynamical Yang-Baxter maps.