K-homology class of the Dirac operator on a compact quantum group
Abstract
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 U(g) a family of Drinfeld twists relating the deformed and classical coproducts can be chosen to be continuous in q.
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