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 is 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.
This video is part of the European Non-Associative Algebra Seminar series.
