engleski

Globalizing Hopf-Galois extensions

Hopf-Galois extensions are noncommutative generalizations of G-principal bundles where both the total space and the base are affine, and the group is replaced by a Hopf algebra. In noncommutative algebraic geometry, we may need the case when the total or base space are not necessarily affine. I will explain how to make sense of gluing together charts which are Hopf-Galois extensions, into noncommutative bundles which may be viewed as a global generalizaton of Hopf-Galois extensions. One of the prerequisites is to explain what the Hopf algebra action on a category of "quasicoherent sheaves" on nonaffine noncommutative scheme is, and what the corresponding "equivariant sheaves" are. The distributive laws for actions of monoidal categories play a major role in generalizations of this picture, like the entwining structures did in affine case.

localization; principal bundles; noncommutative geometry; Hopf algebra; Hopf-Galois extension; equivariant sheaf; distributive laws

Predavanje održano 19 November 2007 u trajanju od dva sata (10:15-12:15).