Atiyah classes and dg-Lie algebroids for matched pairs

Panagiotis Batakidis, Yannick Voglaire

For every Lie pair $(L,A)$ of algebroids we construct a dg-manifold structure on the $\mathbb{Z}$-graded manifold $\mathcal{M}=L[1]\oplus L/A$ such that the inclusion $ι: A[1] \to \…