Quantum Principal Bundles on Quantum Projective Varieties

Abstract: In non commutative geometry, a quantum principal bundle over an affine base is recovered through a deformation of the algebra of its global sections: the property of being a principal bundle is encoded by the notion of Hopf Galois extension, while the local triviality is expressed by the cleft property. We examine the case of a projective base X in the special case X=G/P, where G is a complex semisimple group and P a parabolic subgroup. The quantization of G will then be interpreted as the quantum principal bundle on the quantum base space X, obtained via a quantum section.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar