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arXiv · 1103.5852

The Supergeometry of Loday Algebroids

Janusz Grabowski·David Khudaverdyan·Norbert Poncin
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Abstract

A new 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' associated with a shuffle product 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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Janusz Grabowski, David Khudaverdyan, Norbert Poncin. 2013-04-09. The Supergeometry of Loday Algebroids. https://arxiv.org/abs/1103.5852

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