Lie algebroid cohomology and Lie algebroid extensions
Rings and Algebras
2019-02-12 v1 Algebraic Geometry
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.
Cite
@article{arxiv.1711.05156,
title = {Lie algebroid cohomology and Lie algebroid extensions},
author = {Ettore Aldrovandi and Ugo Bruzzo and Vladimir Rubtsov},
journal= {arXiv preprint arXiv:1711.05156},
year = {2019}
}
Comments
27 pages