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

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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 [math]\displaystyle{ Q }[/math] over a scheme [math]\displaystyle{ (X,\mathcal{O}) }[/math], and a sheaf of finitely generated Lie [math]\displaystyle{ \mathcal{O} }[/math]-algebras [math]\displaystyle{ L }[/math], we determine the obstruction to the existence of extensions [math]\displaystyle{ 0 \to L \to E \to Q \to 0 }[/math], and classify the extensions in terms of a suitable Lie algebroid hypercohomology group.


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