Double Lie algebroids and representations up to homotopy

Published 4 Sep 2014 in math.DG | (1409.1502v2)

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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