• Corpus ID: 119152097

Homotopy Loday Algebras and Symplectic $2$-Manifolds

  title={Homotopy Loday Algebras and Symplectic \$2\$-Manifolds},
  author={Matthew T. Peddie},
  journal={arXiv: Mathematical Physics},
  • M. Peddie
  • Published 9 April 2018
  • Mathematics
  • arXiv: Mathematical Physics
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… 

L-infinity bialgebroids and homotopy Poisson structures on supermanifolds

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

$L_\infty$ and $A_\infty$ structures: then and now

Looking back over 55 years of higher homotopy structures, I reminisce as I recall the early days and ponder how they developed and how I now see them. From the history of $A_\infty$-structures and

L-infinity and A-infinity structures

Looking back over 55 years of higher homotopy structures, I reminisce as I recall the early days and ponder how they developed and how I now see them. From the history of A∞-structures and later of



Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket

We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent Δ operator, we define a non-commutative generalization of the higher Koszul brackets, which are

L-infinity algebras and higher analogues of Dirac structures and Courant algebroids

We define a higher analogue of Dirac structures on a manifold M. Under a regularity assumption, higher Dirac structures can be described by a foliation and a (not necessarily closed, non-unique)

On the structure of graded symplectic supermanifolds and Courant algebroids

This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudo-Euclidean vector bundles

Courant Algebroids and Strongly Homotopy Lie Algebras

Courant algebroids are structures which include as examples the doubles of Lie bialgebras and the direct sum of tangent and cotangent bundles with the bracket introduced by T. Courant for the study

Derived Brackets

We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of

Nonabelian higher derived brackets

Courant algebroids, derived brackets and even symplectic supermanifolds

In this dissertation we study Courant algebroids, objects that first appeared in the work of T. Courant on Dirac structures; they were later studied by Liu, Weinstein and Xu who used Courant

Manin Triples for Lie Bialgebroids

In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does

Derived brackets and sh Leibniz algebras