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arXiv · 1711.05156

Lie algebroid cohomology and Lie algebroid extensions

Ettore Aldrovandi·Ugo Bruzzo·Vladimir Rubtsov
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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,O), and a sheaf of finitely generated Lie O-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.

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BibTeXRIS

Ettore Aldrovandi, Ugo Bruzzo, Vladimir Rubtsov. 2017-11-14. Lie algebroid cohomology and Lie algebroid extensions. https://arxiv.org/abs/1711.05156

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