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 | References | Similar Articles | Additional Information

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 as automorphisms of the Cuntz algebra .

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

Furthermore we give a description of the fixed point subalgebra under the coaction of on 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