# Compact, open subgroups of a quantum group and multiplier Hopf
*-algebras

Abstract: (Joint work with A. Van Daele)
The existence of a multiplier Hopf *-algebra of functions on a locally
compact group G (pointwise product) is equivalent to the existence of a
compact, open subgroup. This is again equivalent to the following: There
are non-zero elements $a\in C^*_r(G)$ and $b\in C_0(G)$ which commute.
We
shall use this to discuss how to characterize compact, open "subgroups"
of
a quantum group and what a totally disconnected quantum group should be.