Actions of compact quantum groups on operator algebras

The notion of compact quantum groups, matrix pseudogroups in original terminology, was first introduced by S. L. Woronowicz on the basis of $C^{*} $-algebra theory [22], and it is the dual notion of Drinfel’d and Jimbo’s quantum universal enveloping algebras [4] [7]. Since it may provide a new kind of symmetry because it generalizes the notio