Cohomology in algebra, geometry, physicsand statistics
Gluing bundles over noncommutative flag varieties
Speaker’s name:
Zoran Skoda
Speaker’s affiliation:
University of Zadar and University of Hradec Kralove
Place:
ZOOM meeting
Date:
Wednesday, 4. November 2020 - 11:30 to 12:30
Abstract:
Localization functors may be used to define local covers in some examples from noncommutative geometry. In an earlier work, I have used this technique to treat gluing of bundles over quantum flag varieties with applications to quantum group coherent states and representation theory. A non-flat version of this technique is under development. A basic series of examples is what I call universal noncommutative flag varieties (including Grassmannians), where no "quantum" relations are imposed. Various classical and quantum flag varieties appear as subvarieties. I will present these the rationale behind these examples and of gluing technique for certain special covers. Main aim is to derive explicit cocycle describing certain tautological bundle over a universal noncommutative Grassmannian leading to noncommutative double ratios studied recently by Retakh, Rubtsov and Sharygin.
