On the Hochschild homology of quantum SL(N)

Details On the Hochschild homology of quantum SL(N) On the Hochschild homology of quantum SL(N)

2005-09-12

arxiv.org/abs/math/0509254v3

Comptes Rendus Acad. Sci. Paris, Ser. I, 343, 9-13 (2006)

Mathematics

Quantum Algebra

5 pages, no figures. Final version accepted for publication

Scientific paper

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 A_sigma, 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 H_{N^2-1} (A, A_sigma)=k, generalizing our previous results for quantum SL(2).

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