We show that the quantized coordinate ring satisfies van den Bergh's analogue of Poincaré duality for Hochschild (co)homology with dualizing bimodule being , the A-bimodule which is A as k-vector space with right multiplication twisted by the modular automorphism σ of the Haar functional. This implies that , generalizing our previous result for .
Nous démontrons que l'anneau standard quantique des coordonnées satisfait l'analogue de van den Bergh de la dualité de Poincaré dans l'(co)homologie de Hochschild. Le bimodule de la dualité est , le A-bimodule qui est A comme un espace vectoriel, avec la multiplication à droite tordue par l'automorphisme modulaire σ de la fonctionnelle de Haar. Ceci implique , et généralise notre résultat précédent pour .
Accepted:
Published online:
Tom Hadfield 1; Ulrich Krähmer 2
@article{CRMATH_2006__343_1_9_0, author = {Tom Hadfield and Ulrich Kr\"ahmer}, title = {On the {Hochschild} homology of quantum $ \mathit{SL}(N)$}, journal = {Comptes Rendus. Math\'ematique}, pages = {9--13}, publisher = {Elsevier}, volume = {343}, number = {1}, year = {2006}, doi = {10.1016/j.crma.2006.03.031}, language = {en}, }
Tom Hadfield; Ulrich Krähmer. On the Hochschild homology of quantum $ \mathit{SL}(N)$. Comptes Rendus. Mathématique, Volume 343 (2006) no. 1, pp. 9-13. doi : 10.1016/j.crma.2006.03.031. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.03.031/
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