FRT Construction for Dynamical Yang-Baxter Maps

2009/12/07 by Shibukawa, Youichi, Takeuchi, Mitsuhiro
#16W35 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0912.1156

Abstract

Notions of an (H, X)-bialgebroid and of its dynamical representation are proposed. The dynamical representations of each (H, X)-bialgebroid form a tensor category. Every dynamical Yang-Baxter map R(lambda) satisfying suitable conditions, a generalization of the set-theoretical solution to the quantum Yang-Baxter equation, gives birth to an (H, X)-bialgebroid A_R. The categories of L-operators for R(lambda) and of dynamical representations of A_R are isomorphic as tensor categories.

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