On quantum semigroup actions on finite quantum spaces

Details On quantum semigroup actions on finite quantum spaces On quantum semigroup actions on finite quantum spaces

2008-10-03

arxiv.org/abs/0810.0596v3

Infin. Dimens. Anal. Qu. 12 no. 3 (2009), 503--509

Mathematics

Operator Algebras

A characterization of actions preserving a faithful state added

Scientific paper

We show that a continuous action of a quantum semigroup $\mathcal{S}$ on a finite quantum space (finite dimensional $\mathrm{C}^*$-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.

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