We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme X, and a coherent sheaf of Lie OX-algebras L, we determine the obstruction to the existence of extensions 0→L→E→Q→0, and classify the extensions in terms of a suitable Lie algebroid hypercohomology group. In the preliminary sections we study free Lie algebroids and recall some basic facts about Lie algebroid hypercohomology.

Lie algebroid cohomology and Lie algebroid extensions / Aldrovandi, E.; Bruzzo, U.; Rubtsov, V.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 505(2018), pp. 456-481. [10.1016/j.jalgebra.2018.03.018]

Lie algebroid cohomology and Lie algebroid extensions

Aldrovandi, E.;Bruzzo, U.;Rubtsov, V.
2018

Abstract

We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme X, and a coherent sheaf of Lie OX-algebras L, we determine the obstruction to the existence of extensions 0→L→E→Q→0, and classify the extensions in terms of a suitable Lie algebroid hypercohomology group. In the preliminary sections we study free Lie algebroids and recall some basic facts about Lie algebroid hypercohomology.
JOURNAL OF ALGEBRA
505
456
481
https://www.sciencedirect.com/science/article/pii/S0021869318301984?via%3Dihub
Aldrovandi, E.; Bruzzo, U.; Rubtsov, V.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/85600
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