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

2016/06/09 by Kamiya, Noriaki, Shibukawa, Youichi
#16T25 #18D10 #20N10 #53C30 (Secondary) #53C35 #81R50 (Primary) 20N05 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1606.02789

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.

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