On the l^2-Betti numbers of universal quantum groups

Abstract

We show that the first ${\ell }^2$-Betti number of the duals of the free unitary quantum groups is one, and that all ${\ell }^2$-Betti numbers vanish for the duals of the quantum automorphism groups of full matrix algebras.

16 pages; v3: accepted for publication in Math. Ann.; following the referee's suggestion Remark 1.8 was made more explicit and turned into Lemma 1.8; a reference to more recent developments on l^2-Betti numbers was added at the end of the article; v2: we remark that l2-Betti numbers of the free unitary quantum groups vanish in degree at least 4, references added, typos corrected

Cited by in corpus (1)

• L^2-Betti numbers of rigid C*-tensor categories and discrete quantum groups