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arXiv · 0903.1686

Homology of free quantum groups

B. Collins·J. Härtel·A. Thom
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Abstract

We compute the Hochschild homology of the free orthogonal quantum group $A_o(n)$. We show that it satisfies Poincar\'e duality and should be considered to be a 3-dimensional object. We then use recent results of R. Vergnioux to derive results about the $\ell^2$-homology of $A_o(n)$ and estimates on the free entropy dimension of its set of generators. In particular, we show that the $\ell^2$ Betti-numbers of $A_o(n)$ all vanish and that the free entropy dimension is less than 1.

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BibTeXRIS

B. Collins, J. Härtel, A. Thom. 2009-03-10. Homology of free quantum groups. https://doi.org/10.1016/j.crma.2009.01.021

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