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arXiv · 1107.1539

Lie algebroid modules and representations up to homotopy

Rajan Amit Mehta
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Abstract

We establish a relationship between two different generalizations of Lie algebroid representations: representation up to homotopy and Vaintrob's Lie algebroid modules. Specifically, we show that there is a noncanonical way to obtain a representation 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. We therefore obtain a one-to-one correspondence, up to equivalence.

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Rajan Amit Mehta. 2011-07-07. Lie algebroid modules and representations up to homotopy. https://doi.org/10.1016/j.indag.2014.07.013

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