Nonabelian holomorphic Lie algebroid extensions

Author(s)

Bruzzo, Ugo ^{[1, 2]} ; Mencattini, Igor ^[3] ; Rubtsov, Vladimir N. ^{[4, 5]} ; Tortella, Pietro ^[3]

Affiliation

^[1] Ist Nazl Fis Nucl, Sez Trieste, Trieste - Italy

^[2] Univ Fed Santa Catarina, Dept Matemat, BR-88040900 Florianopolis, SC - Brazil

^[3] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13566590 Sao Carlos, SP - Brazil

^[4] Univ Angers, UFR Sci, Dept Math, CNRS, LAREMA, UMR 6093, F-49045 Angers 01 - France

^[5] Inst Theoret & Expt Phys, Div Theoret, Moscow 117259 - Russia

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL OF MATHEMATICS; v. 26, n. 5 MAY 2015.
• Web of Science Citations: 4

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. (AU)

• FAPESP's process: 12/07867-7 - Spectral sequencies associated to Lie algebroids
• Grantee: Igor Mencattini
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• FAPESP's process: 11/17593-9 - Holomorphic Lie algebroids, stacks of twisted modules and applications to the Hitchin system and Poisson geometry.
• Grantee: Pietro Tortella
• Support Opportunities: Scholarships in Brazil - Post-Doctoral