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arXiv · 1409.1502

Double Lie algebroids and representations up to homotopy

Alfonso Gracia-Saz·Madeleine Jotz Lean·Kirill C. H. Mackenzie·Rajan A. Mehta
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Abstract

We show that double Lie algebroids, together with a chosen linear splitting, are equivalent to pairs of 2-term representations up to homotopy satisfying compatibility conditions which extend the notion of matched pair of Lie algebroids. We discuss in detail the tangent of a Lie algebroid.

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Alfonso Gracia-Saz, Madeleine Jotz Lean, Kirill C. H. Mackenzie, Rajan A. Mehta. 2014-09-05. Double Lie algebroids and representations up to homotopy. https://doi.org/10.1007/s40062-017-0183-1

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