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