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

Paolucci, Anna

doi:10.1090/S0002-9939-97-03595-8

Coactions of Hopf algebras on Cuntz algebras and their fixed point algebras
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Proc. Amer. Math. Soc. 125 (1997), 1033-1042 Request permission

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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