FRT construction for dynamical Yang-Baxter maps

Notions of an (H. X)-bialgebioid and of its dynamical representation are proposed. The dynamical representations of each (H. X)bralgebroid 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 air (H. X)-bialgebroid A(R). The categories of L-operators for R(lambda) and of dynamical representations of AR are isomorphic as tensor categories, (C) 2009 Elsevier Inc. All rights reserved.