Nonabelian holomorphic Lie algebroid extensions-Reference-Cited by-同舟云学术

Nonabelian holomorphic Lie algebroid extensions

Published:2015-05 Issue:05 Volume:26 Page:1550040
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

Bruzzo Ugo¹²,Mencattini Igor³,Rubtsov Vladimir N.⁴⁵,Tortella Pietro³

Affiliation:

1. Departamento de Matemática, Universidade Federal de Santa Catarina, Campus Universitário Trindade, CEP 88.040-900, Florianópolis, SC, Brazil

2. Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste, Trieste, Italy

3. Instituto de Ciências Matemáticas e de Computação – USP, Avenida Trabalhador São-Carlense, 400 – Centro, CEP 13566-590, São Carlos, SP, Brazil

4. Département de Mathématiques, Université d'Angers, UFR Sciences, LAREMA, UMR 6093 du CNRS, 2 bd. Lavoisier, 49045 Angers Cedex 01, France

5. ITEP Theoretical Division, 25 Bol. Tcheremushkinskaya, 117259, Moscow, Russia

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X15500408

Reference25 articles.

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