The supergeometry of Loday algebroids | Zendy

Janusz Grabowski | Zendy; David Khudaverdyan | Zendy; Norbert Poncin | Zendy

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The supergeometry of Loday algebroids

Author(s) -

Janusz Grabowski,

David Khudaverdyan,

Norbert Poncin

Publication year - 2013

Publication title -

the journal of geometric mechanics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.511

H-Index - 17

eISSN - 1941-4897

pISSN - 1941-4889

DOI - 10.3934/jgm.2013.5.185

Subject(s) - reduction (mathematics) , mathematics , algebraic number , manifold (fluid mechanics) , computer science , pure mathematics , algebra over a field , geometry , mathematical analysis , engineering , mechanical engineering

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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