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 U q (g), and the structure of a co-module algebra over the quantum group G q associated with U q (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.