On quantum semigroup actions on finite quantum spaces

Abstract

We show that a continuous action of a quantum semigroup $\mathcal{S}$ on a finite quantum space (finite dimensional ${\mathrm{C}}^{\ast }$-algebra) preserving a faithful state comes from a continuous action of the quantum Bohr compactification $\mathfrak{b}\mathcal{S}$ of $\mathcal{S}$. Using the classification of continuous compact quantum group actions on $M_2$ we give a complete description of all continuous quantum semigroup actions on this quantum space preserving a faithful state.

A characterization of actions preserving a faithful state added

References in corpus (1)

• Quantum $\mathrm{SO}(3)$ groups and quantum group actions on $M_2$

Cited by in corpus (1)

• Classification of non-Kac compact quantum groups of SU(n) type