L-infinity bialgebroids and homotopy Poisson structures on supermanifolds

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 $(TM,T^{\ast }M)$ has a canonical structure of an $L_{\infty }$-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" $L_{\infty }$-bialgebroid, which is a specialization of a "(quasi)triangular" homotopy Poisson structure. We define both here.

LaTeX, 19 pp

References in corpus (4)

• Graded Geometry, $Q$-Manifolds, and Microformal Geometry
• On homotopy Lie bialgebroids
• Thick morphisms, higher Koszul brackets, and $L_{\infty }$-algebroids
• Homotopy Loday Algebras and Symplectic $2$-Manifolds

Cited by in corpus (2)

• Topological Field Theories induced by twisted R-Poisson structure in any dimension
• On a Batalin--Vilkovisky operator generating higher Koszul brackets on differential forms