Geodesic
K-homology class of the Dirac operator on a compact quantum group
Documenta mathematica, Tome 16 (2011), pp. 767-780
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By a result of Nagy, the C^*-algebra of continuous functions on the q-deformation Gq​ 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 Gq​, 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 Uq​g and Ug a family of Drinfeld twists relating the deformed and classical coproducts can be chosen to be continuous in q.
DOI : 10.4171/dm/351
Classification : 46L80, 58B32, 58B34
Mots-clés : Dirac operator, quantum groups, K-homology 
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     author = {Lars Tuset and Sergey Neshveyev},
     title = {K-homology class of the {Dirac} operator on a compact quantum group},
     journal = {Documenta mathematica},
     pages = {767--780},
     year = {2011},
     volume = {16},
     doi = {10.4171/dm/351},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/351/}
}
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Lars Tuset; Sergey Neshveyev. K-homology class of the Dirac operator on a compact quantum group. Documenta mathematica, Tome 16 (2011), pp. 767-780. doi: 10.4171/dm/351

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