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NONCOMMUTATIVE PRINCIPAL BUNDLES OVER PROJECTIVE BASES AND THEIR DIFFERENTIAL CALCULI
- Speaker(s)
- PAOLO ASCHIERI
- Affiliation
- Università del Piemonte Orientale, Alessandria, Italy
- Date
- March 13, 2024, 5:15 p.m.
- Link
- https://uw-edu-pl.zoom.us/j/95105055663?pwd=TTIvVkxmMndhaHpqMFUrdm8xbzlHdz09
- Information about the event
- 405 IMPAN & ZOOM
- Seminar
- North Atlantic Noncommutative Geometry Seminar
We present a sheaf approach to noncommutative principal bundles, and extend it to differential calculi. This allows us to study the differential geometry of noncommutative bundles over noncommutative projective varieties. The main class of examples is given by covariant calculi over quantum flag manifolds, which we provide via an explicit Ore-extension construction. We next introduce principal covariant calculi by requiring a local compatibility of the calculi on the total sheaf, the base sheaf and the structure Hopf algebra, in terms of exact sequences. The examples of principal (covariant) calculi on the quantum principal bundles SLq(2,C) and GLq(2,C) over the quantum complex projective line are detailed.
