From $L_{\infty }$-algebroids to higher Schouten/Poisson structures

Abstract

We show that $L_{\infty }$-algebroids, understood in terms of Q-manifolds can be described in terms of certain higher Schouten and Poisson structures on graded (super)manifolds. This generalises known constructions for Lie (super)algebras and Lie algebroids.

23 pages. Paper reorganised, typos corrected, various improvements made and extra references added. To appear in Reports on Mathematical Physics

References in corpus (4)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Tulczyjew triples and higher Poisson/Schouten structures on Lie algebroids

Cited by in corpus (15)

• Representations of Homotopy Lie-Rinehart Algebras
• Linear duals of graded bundles and higher analogues of (Lie) algebroids
• On the Strong Homotopy Lie-Rinehart Algebra of a Foliation
• On the Strong Homotopy Associative Algebra of a Foliation
• Shifted derived Poisson manifolds associated with Lie pairs
• Vector Bundle Valued Differential Forms on $\mathbb{N}Q$-manifolds
• Deformation spaces and normal forms around transversals
• Variational tricomplex of a local gauge system, Lagrange structure and weak Poisson bracket
• Dg manifolds, formal exponential maps and homotopy Lie algebras
• Veronese powers of operads and pure homotopy algebras
• Keller admissible triples and Duflo theorem
• Kirillov structures up to homotopy
• Modular classes of Q-manifolds: a review and some applications
• Homological sections of Lie algebroids
• Quantization of (-1)-Shifted Derived Poisson Manifolds