Rubtsov V. Lie algebroid cohomology: from Der to Lie algebroid non-abelian extensions (abstract)

Speaker: Vladimir Rubtsov

Title: Lie algebroid cohomology: from Der to Lie algebroid non-abelian extensions

Abstract:
After a short historical reminder I consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid $Q$ over a scheme $(X,{\mathcal {O}})$, and a sheaf of finitely generated Lie ${\mathcal {O}}$-algebras $L$, we determine the obstruction to the existence of extensions $0\to L\to E\to Q\to 0$, and classify the extensions in terms of a suitable Lie algebroid hypercohomology group.

Video
Slides: RubtsovAMVconf2021slides.pdf

Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.
Alexandre Vinogradov Memorial Conference.