Homology of free quantum groups

We compute the Hochschild homology of the free orthogonal quantum group A(0)(n). We show that it satisfies Poincare duality and should be considered to be a 3-dimensional object. We then use recent results of R. Vergnioux to derive results about the l(2)-homology of A(0)(n) and estimates on the free entropy dimension of its set of generators. In particular, we show that the l(2) Betti-numbers of A(0)(n) all vanish and that the free entropy dimension is less than 1. To cite this article: B. Collins et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights, reserved.