Homotopy Loday Algebras and Symplectic $2$-Manifolds

Abstract

Using the technique of higher derived brackets developed by Voronov, we construct a homotopy Loday algebra in the sense of Ammar and Poncin associated to any symplectic $2$-manifold. The algebra we obtain has a particularly nice structure, in that it accommodates the Dorfman bracket of a Courant algebroid as the binary operation in the hierarchy of operations, and the defect in the symmetry of each operation is measurable in a certain precise sense. We move to call such an algebra a homotopy Dorfman algebra, or a $D_{\infty }$-algebra, which leads to the construction of a homotopy Courant algebroid.

References in corpus (7)

• Higher derived brackets and homotopy algebras
• Courant algebroids, derived brackets and even symplectic supermanifolds
• Derived brackets
• Courant Algebroids and Strongly Homotopy Lie Algebras
• Lagrange structure and quantization
• Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket
• Nonabelian higher derived brackets

Cited by in corpus (1)

• L-infinity bialgebroids and homotopy Poisson structures on supermanifolds