On homotopy Lie bialgebroids

Abstract

A well-known result of A. Vaintrob characterizes Lie algebroids and their morphisms in terms of homological vector fields on supermanifolds. We give an interpretation of Lie bialgebroids and their morphisms in terms of odd symplectic dg-manifolds, building on the approach of D. Roytenberg. This extends naturally to the homotopy Lie case and leads to the notion of $L_{\infty }$-bialgebroids and $L_{\infty }$-morphisms between them.

21 pages, 1 figure; the new version is significantly revised

References in corpus (1)

• How Dennis realized he had `invented' $L_{\infty }$-algebras a.k.a. strongly homotopy Lie algebras

Cited by in corpus (3)

• On a Batalin--Vilkovisky operator generating higher Koszul brackets on differential forms
• L-infinity bialgebroids and homotopy Poisson structures on supermanifolds
• Homotopy Poisson algebras, Maurer-Cartan elements and Dirac structures of CLWX 2-algebroids