Braided tensor C*-categories, Hecke symmetries and actions on extended Cuntz algebras

In this paper we deal with braided tensor C*-categories. For every object of the category we associate a C*-algebra denoted by . An analysis of the braiding is carried out by using the conjugate equations. If the braiding is a Hecke symmetry and the -dimension is appropriately chosen, we characterize the C*-algebra as the one generated by the representation given by the Markov trace. This analysis leads to the existence of an action of on . Such actions (Theorem 1) correspond to *-monomorphisms of on which generalize the ones obtained earlier by the author (1997).