Vb–algebroids and Representation Theory of Lie Algebroids Alfonso Gracia-saz and Rajan
نویسنده
چکیده
A VB–algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB–algebroids and certain flat Lie algebroid superconnections, up to a natural notion of equivalence. In this setting, we are able to construct characteristic classes, which in special cases reproduce characteristic classes constructed by Crainic and Fernandes. We give a complete classification of regular VB–algebroids, and in the process we obtain another characteristic class of Lie algebroids that does not appear in the ordinary representation theory of Lie algebroids.
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