Double Lie algebroids and representations up to homotopy

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.

References in corpus (1)

• VB-algebroid morphisms and representations up to homotopy

Cited by in corpus (4)

• The Geometrisation of $\mathbb{N}$-manifolds of degree 2
• Lie 2-algebroids and matched pairs of 2-representations - a geometric approach
• $A_{\infty }$-Algebras from Lie Pairs
• Categorification of VB-Lie algebroids and VB-Courant algebroids