The canonical central exact sequence for locally compact quantum groups

Abstract

For a locally compact quantum group $\mathbb{G}$ we define its center, $\mathcal{Z}(\mathbb{G})$, and its quantum group of inner automorphisms, $\mathrm{Inn}(\mathbb{G})$. We show that one obtains a natural isomorphism between $\mathrm{Inn}(\mathbb{G})$ and $\mathbb{G}/\mathcal{Z}(\mathbb{G})$, we characterize normal quantum subgroups of a compact quantum group as those left invariant by the action of the quantum group of inner automorphisms and discuss several examples.

arXiv commentv4: 14 pages, modified title. The final version of the paper will appear in Mathematische Nachrichten