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Abstract

In this paper we will, first, give a local splitting theorem for Lie algebroids which shows that we have a splitting in the product of a tangent bundle and a rank 0 Lie algebroid. We give a very simple way to prove the unicity of the transversal structures. We also give a linearization theorem for these rank 0 algebroids. All these results are part of the “folklore” of the domain and are not very difficult, but, to my present knowledge, they are unavailable in the literature.