English

Nonabelian holomorphic Lie algebroid extensions

Symplectic Geometry 2017-08-31 v3 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.1305.2377,
  title  = {Nonabelian holomorphic Lie algebroid extensions},
  author = {Ugo Bruzzo and Igor Mencattini and Vladimir Rubtsov and Pietro Tortella},
  journal= {arXiv preprint arXiv:1305.2377},
  year   = {2017}
}

Comments

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

R2 v1 2026-06-22T00:14:38.796Z