2005/01/07 by Iakovos Androulidakis, Androulidakis, Iakovos
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons
paper · doi:10.48550/arxiv.math/0501103
openalex publication_date 2005/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citeKCHM:new.