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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Coactions of Hopf algebras on Cuntz algebras
and their fixed point algebras


Author: Anna Paolucci
Journal: Proc. Amer. Math. Soc. 125 (1997), 1033-1042
MSC (1991): Primary 46M05, 16W30, 81R50
DOI: https://doi.org/10.1090/S0002-9939-97-03595-8
MathSciNet review: 1350959
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Abstract: We study coactions of Hopf algebras coming from compact quantum groups on the Cuntz algebra. These coactions are the natural generalization to the coalgebra setting of the canonical representation of the unitary matrix group $U(d)$ as automorphisms of the Cuntz algebra $O_d$.

In particular we study the fixed point subalgebra under the coaction of the quantum compact groups $U_q(d)$ on the Cuntz algebra $O_d$ by extending to any dimension $d<\infty $ a result of Konishi (1992).

Furthermore we give a description of the fixed point subalgebra under the coaction of $SU_q(d)$ on $O_d$ in terms of generators.


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Additional Information

Anna Paolucci
Affiliation: The Fields Institute, 185 Columbia St. West, Waterloo, Ontario, Canada N2L 5Z5
Address at time of publication: School of Mathematics, University of Leeds, LS2 9JT United Kingdom
Email: paolucci@amsta.leeds.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-97-03595-8
Keywords: $C^*$-algebras, Hilbert spaces, representation, corepresentation, duality
Received by editor(s): August 4, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society