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

TL;DR

This paper introduces a novel connection between s-sets, a generalization of symmetric spaces, and dynamical Yang-Baxter maps, leading to new algebraic structures like Hopf algebroids and tensor categories.

Contribution

It establishes that suitable s-sets can generate dynamical Yang-Baxter maps and constructs associated Hopf algebroids and tensor categories, expanding the algebraic framework of quantum integrable systems.

Findings

S-sets can produce dynamical Yang-Baxter maps

Construction of Hopf algebroids from these maps

Development of rigid tensor categories

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.