# Homotopy Loday Algebras and Symplectic $2$-Manifolds

@article{Peddie2018HomotopyLA, title={Homotopy Loday Algebras and Symplectic \$2\$-Manifolds}, author={Matthew T. Peddie}, journal={arXiv: Mathematical Physics}, year={2018} }

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…

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