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On the Hochschild homology of quantum SL(N)

Tom Hadfield·Ulrich Kraehmer
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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 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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Tom Hadfield, Ulrich Kraehmer. 2006-05-19. On the Hochschild homology of quantum SL(N). https://arxiv.org/abs/math/0509254

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