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

Paolucci, Anna

doi:10.1090/S0002-9939-99-04693-6

Braided tensor C*-categories, Hecke symmetries and actions on extended Cuntz algebras
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Proc. Amer. Math. Soc. 127 (1999), 2249-2258 Request permission

Abstract:

In this paper we deal with braided tensor C*-categories. For every object $\rho$ of the category we associate a C*-algebra denoted by $O_\rho$. An analysis of the braiding is carried out by using the conjugate equations. If the braiding is a Hecke symmetry and the $q$-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 $\mathcal {F}_{SU_q\left ( d\right ) }$ on $O_\rho$. Such actions (Theorem 1) correspond to *-monomorphisms of $\left ( O_N\right ) ^{SU_q\left ( d\right ) }$ on $O_\rho$ which generalize the ones obtained earlier by the author (1997).

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