Leibniz algebroids, twistings and exceptional generalized geometry

Details Leibniz algebroids, twistings and exceptional generalized geometry Leibniz algebroids, twistings and exceptional generalized geometry

2011-01-05

arxiv.org/abs/1101.0856v2

Journal of Geometry and Physics 62 (2012), pp. 903-934

Mathematics

Differential Geometry

58 pages

Scientific paper

10.1016/j.geomphys.2012.01.007

We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a construction starting from graded Lie algebras. In this case the Leibniz bracket is a derived bracket and there are higher derived brackets resulting in an $L_\infty$-structure. The algebroids can be twisted by a non-abelian cohomology class and we prove that the twisting class is described by a Maurer-Cartan equation. For compact manifolds we construct a Kuranishi moduli space of this equation which is shown to be affine algebraic. We explain how these results are related to exceptional generalized geometry.

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