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arXiv · 1804.03025

Homotopy Loday Algebras and Symplectic $2$-Manifolds

Matthew T. Peddie
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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.

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Matthew T. Peddie. 2018-04-09. Homotopy Loday Algebras and Symplectic $2$-Manifolds. https://arxiv.org/abs/1804.03025

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