Geodesic
Algebra/Homological Algebra
On the Hochschild homology of quantum SL(N)
[Sur l'homologie de Hochschild de quantum SL(N)]

Présenté par : Alain Connes

Hadfield, Tom1 ; Krähmer, Ulrich2
1 School of Mathematical Sciences, Queen Mary, University of London, 327 Mile End Road, London E1 4NS, UK
2 Instytut Matematyczny Polskiej Akademii Nauk, Ul. Sniadeckich 8, 00956 Warszawa, Poland
Comptes Rendus. Mathématique, Tome 343 (2006) no. 1, pp. 9-13.

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We show that the quantized coordinate ring A:=kq[SL(N)] satisfies van den Bergh's analogue of Poincaré duality for Hochschild (co)homology with dualizing bimodule being Aσ, 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 HN2−1(A,Aσ)≅k, generalizing our previous result for kq[SL(2)].

Nous démontrons que l'anneau standard quantique des coordonnées A:=kq[SL(N)] satisfait l'analogue de van den Bergh de la dualité de Poincaré dans l'(co)homologie de Hochschild. Le bimodule de la dualité est Aσ, 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 HN2−1(A,Aσ)≅k, et généralise notre résultat précédent pour kq[SL(2)].

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.03.031

Hadfield, Tom 1 ; Krähmer, Ulrich 2

1 School of Mathematical Sciences, Queen Mary, University of London, 327 Mile End Road, London E1 4NS, UK
2 Instytut Matematyczny Polskiej Akademii Nauk, Ul. Sniadeckich 8, 00956 Warszawa, Poland 
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Hadfield, Tom; Krähmer, Ulrich. On the Hochschild homology of quantum $ \mathit{SL}(N)$. Comptes Rendus. Mathématique, Tome 343 (2006) no. 1, pp. 9-13. doi : 10.1016/j.crma.2006.03.031. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2006.03.031/

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