Loday algebroids and their supergeometric interpretation

Details Loday algebroids and their supergeometric interpretation Loday algebroids and their supergeometric interpretation

2011-03-30

arxiv.org/abs/1103.5852v1

Mathematics

Differential Geometry

27 pages

Scientific paper

A concept of Loday algebroid (and its pure algebraic version - Loday pseudoalgebra) is proposed and discussed in comparison with other similar structures present in the literature. The structure of a Loday pseudoalgebra and its natural reduction to a Lie pseudoalgebra is studied. Further, Loday algebroids are interpreted as homological vector fields on a "supercommutative manifold" and the corresponding Cartan calculus is introduced. Several examples, including Courant algebroids, Grassmann-Dorfman and twisted Courant-Dorfman brackets, as well as algebroids induced by Nambu-Poisson structures, are given.

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