# 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 [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.*