Compact quantum group structures on type-I C^*-algebras

We prove a number of results having to do with equipping type-I C^*-algebras with compact quantum group structures, the two main ones being that such a compact quantum group is necessarily co-amenable, and that if the C^*-algebra in question is an extension of a non-zero finite direct sum of elementary C^*-algebras by a commutative unital C^*-algebra then it must be finite-dimensional.