Lie algebroid modules and representations up to homotopy

Details Lie algebroid modules and representations up to homotopy Lie algebroid modules and representations up to homotopy

2011-07-07

arxiv.org/abs/1107.1539v2

Mathematics

Differential Geometry

Scientific paper

We explain how Lie algebroid modules in the sense of Vaintrob provide geometric models for Lie algebroid representations up to homotopy. Specifically, we show that there is a noncanonical way to obtain representations up to homotopy from a given Lie algebroid module, and that any two representations up to homotopy obtained in this way are equivalent in a natural sense. This result extends the relationship between VB-algebroids and 2-term representations up to homotopy, as studied by Gracia-Saz and the author. We also extend the construction of VB-algebroid characteristic classes to the setting of Lie algebroid modules.

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