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

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- by Anna Paolucci
- Proc. Amer. Math. Soc.
**125**(1997), 1033-1042 - DOI: https://doi.org/10.1090/S0002-9939-97-03595-8
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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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## Bibliographic 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
- Received by editor(s): August 4, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- 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