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

Voigt, C. and Yuncken, R. (2015) Equivariant Fredholm modules for the full quantum flag manifold of SUq(3). Documenta Mathematica, 20, pp. 433-490.

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Abstract

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

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Voigt, Dr Christian
Authors: Voigt, C., and Yuncken, R.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Documenta Mathematica
Publisher:Deutsche Mathematiker Vereinigung
ISSN:1431-0635
ISSN (Online):1431-0643
Copyright Holders:Copyright © 2015 Deutsche Mathematiker Vereinigung
First Published:First published in Documenta Mathematica 20:433-490
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
640411Quantum groups and noncommutative geometryChristian VoigtEngineering & Physical Sciences Research Council (EPSRC)EP/L013916/1M&S - MATHEMATICS