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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.
https://hal.archives-ouvertes.fr/hal-01392119 Contributor : Okina Univ AngersConnect in order to contact the contributor Submitted on : Sunday, January 23, 2022 - 4:55:45 PM Last modification on : Thursday, February 3, 2022 - 10:13:42 AM Long-term archiving on: : Sunday, April 24, 2022 - 6:07:40 PM
Ugo Bruzzo, Igor Mencattini, Vladimir Roubtsov, Pietro Tortella. Nonabelian holomorphic Lie algebroid extensions. International Journal of Mathematics, World Scientific Publishing, 2015, 26 (5), ⟨10.1142/S0129167X15500408⟩. ⟨hal-01392119⟩