Crossed modules and the integrability of Lie brackets
Differential Geometry
2008-07-01 v2
Abstract
We show that the integrability obstruction of a transitive Lie algebroid coincides with the lifting obstruction of a crossed module of groupoids associated naturally with the given algebroid. Then we extend this result to general extensions of integrable transitive Lie algebroids by Lie algebra bundles. Such a lifting obstruction is directly related with the classification of extensions of transitive Lie groupoids. We also give a classification of such extensions which differentiates to the classification of transitive Lie algebroids discussed in \cite{KCHM:new}.
Cite
@article{arxiv.math/0501103,
title = {Crossed modules and the integrability of Lie brackets},
author = {Iakovos Androulidakis},
journal= {arXiv preprint arXiv:math/0501103},
year = {2008}
}
Comments
34 pages, revised version. New abstract and introduction. Added examples and remarks