K-homology class of the Dirac operator on a compact quantum group

2011/02/01 by Sergey Neshveyev, Neshveyev, Sergey, Lars Tuset +1
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA

paper · pdf · doi:10.48550/arxiv.1102.0248

10 pages

arxiv created 2011/02/01 · arxiv updated 2011/02/02

Abstract

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.

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