Homology of free quantum groups

Abstract

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.