Nonabelian holomorphic Lie algebroid extensions

Ugo Bruzzo (1) , Igor Mencattini (2) , Vladimir Roubtsov (3) , Pietro Tortella (2)

1 INFN, Sezione di Trieste - Istituto Nazionale di Fisica Nucleare, Sezione di Trieste
2 ICMC-USP - Instituto de Ciências Mathemàticas e de Computação [São Carlos]
3 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

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.

Mots clés: Hodge structure; Lie algebroids; nonabelian extensions; spectral sequences

Domaines: Mathématiques [math]

Ugo Bruzzo, Igor Mencattini, Vladimir Roubtsov, Pietro Tortella. Nonabelian holomorphic Lie algebroid extensions. International Journal of Mathematics, 2015, 26 (5), ⟨10.1142/S0129167X15500408⟩. ⟨hal-01392119⟩