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Lie algebroid cohomology and Lie algebroid extensions
Ettore Aldrovandi, Ugo Bruzzo, Vladimir Rubtsov
We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme (X,O), and a sheaf of finitely generated Lie O-al…
Noncommutative Painlevé equations and systems of Calogero type
Marco Bertola, Mattia Cafasso, Vladimir Roubtsov
All Painlevé equations can be written as a time-dependent Hamiltonian system, and as such they admit a natural generalization to the case of several particles with an interaction o…
Algebras of quantum monodromy data and decorated character varieties
Leonid Chekhov, Marta Mazzocco, Vladimir Rubtsov
The Riemann-Hilbert correspondence is an isomorphism between the de Rham moduli space and the Betti moduli space, defined by associating to each Fuchsian system its monodromy repre…