Geodesic
Equivariant Fredholm modules for the full quantum flag manifold of $\mathrm{SU}_q(3)$
Documenta mathematica, Tome 20 (2015), pp. 433-490.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\{SU}_q(3)$.
Classification : 20G42, 46L80, 19K35
Keywords: noncommutative geometry, quantum groups, quantum flag manifolds, Poincaré duality, Bernstein-Gelfand-Gelfand complex, kasparov theory, baum-connes conjecture 
@article{DOCMA_2015__20__a29,
     author = {Voigt, Christian and Yuncken, Robert},
     title = {Equivariant {Fredholm} modules for the full quantum flag manifold of $\mathrm{SU}_q(3)$},
     journal = {Documenta mathematica},
     pages = {433--490},
     publisher = {mathdoc},
     volume = {20},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a29/}
}
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Voigt, Christian; Yuncken, Robert. Equivariant Fredholm modules for the full quantum flag manifold of $\mathrm{SU}_q(3)$. Documenta mathematica, Tome 20 (2015), pp. 433-490. http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a29/