Quantum group actions on the Cuntz algebra

Abstract

The Cuntz algebra carries in a natural way the structure of a module algebra over the quantized universal enveloping algebra Uq(g), and the structure of a co-module algebra over the quantum group Gq associated with Uq(g). We determine the fixed and co-fixed point algebras in the case of the classical quantum algebras and groups. We also show that the Hopf algebraic structure of the classical quantum groups can be recovered from a knowledge of the co-fixed point algebras.