The Supergeometry of Loday Algebroids
Differential Geometry
2013-04-10 v2 Mathematical Physics
math.MP
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.1103.5852,
title = {The Supergeometry of Loday Algebroids},
author = {Janusz Grabowski and David Khudaverdyan and Norbert Poncin},
journal= {arXiv preprint arXiv:1103.5852},
year = {2013}
}
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29 pages