University of Sydney Algebra Seminar

Ruibin Zhang (University of Sydney)

Friday 26th August, 12.05-12.55pm, Carslaw 275

Quantum supergroups and non-commutative vector bundles

We study quantum analogues of homogeneous vector bundles in the context of quantum supergroups. The space of holomorphic sections is promoted to a left exact covariant functor from the category of locally finite modules over a quantum parabolic subgroup to the category of locally finite modules over the quantum supergroup. The right derived functors of this functor provides a form of Dolbeault cohomology for quantum homogeneous supervector bundles. The cohomology groups of bundles arising from the quantum general linear supergroup are studied in detail.