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

Author: Anna Paolucci
Journal: Proc. Amer. Math. Soc. 127 (1999), 2249-2258
MSC (1991): Primary 46M05, 16W30, 81R50
Published electronically: April 16, 1999
MathSciNet review: 1476384
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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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Additional Information

Anna Paolucci
Affiliation: School of Mathematics, University of Leeds, LS2 9JT, United Kingdom
Address at time of publication: Dipartimento di Matematica, Università di Torino, via Carlo Alberto, 10, 10124 Torino, Italy

Keywords: C*-algebras, Hilbert spaces, Hecke symmetries, braided C*-categories.
Received by editor(s): July 22, 1997
Received by editor(s) in revised form: August 11, 1997, August 18, 1997, and September 11, 1997
Published electronically: April 16, 1999
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1999 American Mathematical Society

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