Mathematics – Quantum Algebra
Scientific paper
2003-11-07
J. Pure Appl. Algebra 191 (2004), no. 3, 285--314.
Mathematics
Quantum Algebra
24 pages
Scientific paper
Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant functor from a category of modules over a quantum parabolic sub-supergroup to the category of locally finite modules of the quantum general linear supergroup. The right derived functors of this functor provides a form of Dolbeault cohomology for quantum homogeneous supervector bundles. We explicitly compute the cohomology groups, which are given in terms of well understood modules over the quantized universal enveloping algebra of the general linear superalgebra.
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