Alessandro Carotenuto

Connections on vector bundles are a fundamental tool in classical differential geometry. When we generalize their definition to noncommutative differential geometry, we are led to consider bimodule connections. In this talk I will present a construction of bimodule connections for line bundles over a large class of quantum homogeneous spaces, namely the quantum flag manifolds. Generalizing the work of Beggs and Majid for the Podles sphere, we realize bimodule connections as associated to a principal connection for the Heckenberger-Kolb calculus . Time allowing, I will review explicit presentations of the associated bimodule maps first in terms of generalised quantum determinants and then in terms of Takeuchi's categorical equivalence for relative Hopf modules.

Bimodule connections for line bundles over irreducible quantum flag manifolds

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