Leibniz algebroids, twistings and exceptional generalized geometry

Abstract

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.

58 pages

References in corpus (8)

• Generalised Geometry for M-Theory
• Generalized complex geometry
• New aspects of the ddc-lemma
• Special metric structures and closed forms
• Higher derived brackets
• On higher analogues of Courant algebroids
• L-infinity algebras and higher analogues of Dirac structures and Courant algebroids
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