Crossed modules and the integrability of Lie brackets

Iakovos Androulidakis

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Crossed modules and the integrability of Lie brackets

Iakovos Androulidakis

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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}.

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Iakovos Androulidakis. 2006-09-25. Crossed modules and the integrability of Lie brackets. https://arxiv.org/abs/math/0501103

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