Nonabelian holomorphic Lie algebroid extensions

TL;DR

This paper classifies nonabelian extensions of holomorphic Lie algebroids and introduces a spectral sequence that generalizes Hochschild-Serre, with applications to the hypercohomology of Atiyah algebroids.

Contribution

It provides a classification of nonabelian holomorphic Lie algebroid extensions and develops a spectral sequence generalizing Hochschild-Serre to this setting.

Findings

Spectral sequence generalizes Hochschild-Serre for holomorphic Lie algebroids

Hypercohomology of Atiyah algebroid has a natural Hodge structure

Classification of nonabelian extensions in the holomorphic category

Abstract

We classify nonabelian extensions of Lie algebroids in the holomorphic category. Moreover we study a spectral sequence associated to any such extension. This spectral sequence generalizes the Hochschild-Serre spectral sequence for Lie algebras to the holomorphic Lie algebroid setting. As an application, we show that the hypercohomology of the Atiyah algebroid of a line bundle has a natural Hodge structure.