L-infinity bialgebroids and homotopy Poisson structures on supermanifolds

2019/09/11 by Voronov, Theodore
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.04914

Abstract

We generalize to the homotopy case a result of K. Mackenzie and P. Xu on relation between Lie bialgebroids and Poisson geometry. For a homotopy Poisson structure on a supermanifold M, we show that (TM, T^*M) has a canonical structure of an L_∞-bialgebroid. (Higher Koszul brackets on forms introduced earlier by H. Khudaverdian and the author are part of one of its manifestations.) The underlying general construction is that of a "(quasi)triangular" L_∞-bialgebroid, which is a specialization of a "(quasi)triangular" homotopy Poisson structure. We define both here.

Related

• Thick morphisms, higher Koszul brackets, and L_∞-algebroids
• Courant algebroids, derived brackets and even symplectic supermanifolds
• Quasi-Lie bialgebroids and twisted Poisson manifolds
• On homotopy Lie bialgebroids
• On Lie superalgebroids of Poisson type