On the Hochschild homology of quantum SL(N)
Abstract
We show that the standard quantized coordinate ring A of quantum SL(N) satisfies van den Bergh's analogue of Poincare duality for Hochschild (co)homology with dualizing bimodule being Asigma, the A-bimodule which is A as k-vector space with right multiplication twisted by the modular automorphism sigma of the Haar functional. This implies that HN2-1 (A, Asigma)=k, generalizing our previous results for quantum SL(2).
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