Exponential map and L∞ algebra associated to a Lie pair

Camille Laurent-Gengoux (1) , Mathieu Stiénon , Ping Xu

1 LMAM - Laboratoire de Mathématiques et Applications de Metz

In this note, we unveil homotopy-rich algebraic structures generated by the Atiyah classes relative to a Lie pair (L,A) of algebroids. In particular, we prove that the quotient L/A of such a pair admits an essentially canonical homotopy module structure over the Lie algebroid A, which we call Kapranov module.

Domaines: Mathématiques [math]

Camille Laurent-Gengoux, Mathieu Stiénon, Ping Xu. Exponential map and L∞ algebra associated to a Lie pair. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2012, pp.817-821. ⟨hal-01093339⟩