Algebraic constructions in the category of vector bundles

Details Algebraic constructions in the category of vector bundles Algebraic constructions in the category of vector bundles

2011-01-05

arxiv.org/abs/1101.0956v3

Mathematics

Differential Geometry

29 pages

Scientific paper

The category of generalized Lie algebroids is presented. We obtain an exterior di?erential calculus for generalized Lie algebroids. In particular, we obtain similar results with the classical and modern results for Lie algebroids. So, a new result of Maurer-Cartan type is presented. Supposing that any vector subbundle of the pullback vector bundle of a generalized Lie algebroid is called interior di?erential system (IDS) for that generalized Lie algebroid, a theorem of Cartan type is obtained. Extending the classical notion of exterior di?erential system (EDS) to generalized Lie algebroids, a theorem of Cartan type is obtained. Using the theory of linear connections of Ehresmann type presented in the paper [1], the identities of Cartan and Bianchi type are presented.

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