EQUIVARIANT FREDHOLM MODULES FOR THE FULL QUANTUM FLAG MANIFOLD OF SUq(3)

作者：Voict Christian^*; Yuncken Robert

来源：Documenta Mathematica, 2015, 20: 433-490.

• Noncommutative geometry
• quantum groups
• quantum flag manifolds
• Poincare duality
• Bernstein-Gelfand-Gelfand complex
• Kasparov theory
• Baum-Connes Conjecture

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 chi(q) = 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 chi(q) satisfies Poincare 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).

• 出版日期2015