We prove that the zeroth L²-Betti number of a compact quantum group vanishes unless the underlying C*-algebra is finite dimensional and that the zeroth L²-homology itself is nontrivial exactly when the quantum group is coamenable.
We prove that the zeroth L²-Betti number of a compact quantum group vanishes unless the underlying C*-algebra is finite dimensional and that the zeroth L²-homology itself is nontrivial exactly when the quantum group is coamenable.