Geodesic
K-homology class of the Dirac operator on a compact quantum group
Documenta mathematica, Tome 16 (2011), pp. 767-780.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: By a result of Nagy, the C^*-algebra of continuous functions on the $q$-deformation $G_q$ of a simply connected semisimple compact Lie group $G$ is KK-equivalent to $C(G)$. We show that under this equivalence the K-homology class of the Dirac operator on $G_q$, which we constructed in an earlier paper, corresponds to that of the classical Dirac operator. Along the way we prove that for an appropriate choice of isomorphisms between completions of $U_q\g$ and $U\g$ a family of Drinfeld twists relating the deformed and classical coproducts can be chosen to be continuous in $q$.
Classification : 58B34, 58B32, 46L80
Keywords: quantum groups, Dirac operator, K-homology 
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     author = {Neshveyev, Sergey and Tuset, Lars},
     title = {K-homology class of the {Dirac} operator on a compact quantum group},
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     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2011__16__a7/}
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Neshveyev, Sergey; Tuset, Lars. K-homology class of the Dirac operator on a compact quantum group. Documenta mathematica, Tome 16 (2011), pp. 767-780. http://geodesic.mathdoc.fr/item/DOCMA_2011__16__a7/