Lie algebroid cohomology as a derived functor

TL;DR

This paper demonstrates that Lie algebroid cohomology can be formulated as a derived functor, enabling new insights into spectral sequences related to Lie algebroid extensions.

Contribution

It introduces a novel perspective by expressing Lie algebroid cohomology as a derived functor, facilitating advanced spectral sequence analysis.

Findings

Cohomology expressed as a derived functor

Spectral sequence for Lie algebroid extensions analyzed

New tools for Lie algebroid cohomology studies

Abstract

We show that the hypercohomology of the Chevalley-Eilenberg-de Rham complex of a Lie algebroid L over a scheme with coefficients in an L-module can be expressed as a derived functor. We use this fact to study a Hochschild-Serre type spectral sequence attached to an extension of Lie algebroids.