engleski

Hopf torsors over corings

A noncommutative space can often be presented by a noncommutative cover by affines, i.e. by spaces represented by noncommutative algebras. Such a cover can be presented by a coring with a distinguished group like element, as in the 1998 work of Kontsevich and Rosenberg. Given such a cover and a Hopf algebra H, I will present a generalization of cleft H-comodule algebras over a base space presented by a cover, where the total space is also given by a cover, together with an appropriate version of a coaction of H. Such a Spec(H)-torsor can be equivalently given by a new kind of Čech like cocycle data over the base. This concept is studied in a work in progress with Tomasz Brzeziński.

noncommutative cover ; coring ; torsor ; Čech cocycle ; Hopf algebra ; cleft comodule algebra ; descent theory

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