ON QUANTUM SEMIGROUP ACTIONS ON FINITE QUANTUM SPACES

Abstract

We show that a continuous action of a quantum semigroup [Formula: see text] on a finite quantum space (finite dimensional C*-algebra) preserving a faithful state comes from a continuous action of the quantum Bohr compactification [Formula: see text] of [Formula: see text]. Using the classification of continuous compact quantum group actions on M2, we give a complete description of all continuous quantum semigroup actions on this quantum space preserving a faithful state.