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Leibniz algebroids, twistings and exceptional generalized geometry

Baraglia, David

Description

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∞-structure. The algebroids can be twisted by a non-abelian cohomology class and we prove that the twisting class...[Show more]

dc.contributor.authorBaraglia, David
dc.date.accessioned2015-12-10T23:25:12Z
dc.identifier.issn0393-0440
dc.identifier.urihttp://hdl.handle.net/1885/67530
dc.description.abstractWe 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∞-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.
dc.publisherElsevier
dc.sourceJournal of Geometry and Physics
dc.subjectKeywords: Exceptional generalized geometry; Leibniz algebroid; Twisted cohomology
dc.titleLeibniz algebroids, twistings and exceptional generalized geometry
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume62
dc.date.issued2012
local.identifier.absfor010000 - MATHEMATICAL SCIENCES
local.identifier.ariespublicationf5625xPUB1471
local.type.statusPublished Version
local.contributor.affiliationBaraglia, David, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.issue5
local.bibliographicCitation.startpage903
local.bibliographicCitation.lastpage934
local.identifier.doi10.1016/j.geomphys.2012.01.007
dc.date.updated2016-02-24T08:47:06Z
local.identifier.scopusID2-s2.0-84857011258
local.identifier.thomsonID000301554400006
CollectionsANU Research Publications

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