Equivariant Fredholm modules for the full quantum flag manifold of SU_q(3)

2014/12/11 by Voigt, Christian, Yuncken, Robert · 1 citation
#19K35 (Secondary) #20G42 (Primary) #46L80 #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1412.3686

Abstract

We introduce C^*-algebras associated to the foliation structure of a quantum flag manifold. We use these to construct SL_q(3,ℂ)-equivariant Fredholm modules for the full quantum flag manifold X_q = SU_q(3)/T of SU_q(3), based on an analytical version of the Bernstein-Gelfand-Gelfand complex. As a consequence we deduce that the flag manifold X_q satisfies Poincaré duality in equivariant KK -theory. Moreover, we show that the Baum-Connes conjecture with trivial coefficients holds for the discrete quantum group dual to SU_q(3).

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