Poincaré--Birkhoff--Witt isomorphisms and Kapranov dg-manifolds

Camille Laurent-Gengoux, Mathieu Stiénon, Ping Xu

We prove that to every inclusion $A\hookrightarrow L$ of Lie algebroids over the same base manifold $M$ corresponds a Kapranov dg-manifold structure on $A[1]\oplus L/A$, which is c…