Nonabelian holomorphic Lie algebroid extensions

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.

22 pages. v2: 26 pages. The material has been reorganized and the exposition improved. Slightly modified title. v3: Typos corrected, exposition streamlined, introduction rewritten