Hopf algebroids and rigid tensor categories associated with dynamical Yang-Baxter maps (Q907347)

Solutions of the quantum Yang-Baxter equation give rise to a class of Hopf algebras, called quantum groups, via the FRT construction. Similarly, Hopf algebroids arise as dynamical quantum groups based on the quantum dynamical Yang-Baxter equation ([\textit{P. Etingof} and \textit{A. Varchenko}, Commun. Math. Phys. 196, No. 3, 591--640 (1998; Zbl 0957.17019)]). The author constructs Hopf algebroids from set-theoretic solutions. Modifying previous constructions [the author and \textit{M. Takeuchi} [J. Algebra 323, No. 6, 1698--1728 (2010; Zbl 1193.18005)], two rigid tensor categories with finite dimensional objects are defined. An isomorphism of both tensor categories is given by a strict tensor functor.