Leibniz Algebras, Courant Algebroids, and Multiplications on Reductive Homogeneous Spaces

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dc.creatorKinyon, Michael K.
dc.creatorWeinstein, Alan
dc.date2000-06-04
dc.date2000-07-06
dc.date.accessioned2026-07-07T04:35:42Z
dc.date.available2026-07-07T04:35:42Z
dc.descriptionWe show that the skew-symmetrized product on every Leibniz algebra E can be realized on a reductive complement to a subalgebra in a Lie algebra. As a consequence, we construct a nonassociative multiplication on E which, when E is a Lie algebra, is derived from the integrated adjoint representation. We apply this construction to realize the bracket operations on the sections of Courant algebroids and on the ``omni-Lie algebras'' recently introduced by the second author.
dc.description24 pages. Version 2 has minor corrections
dc.identifierhttps://arxiv.org/abs/math/0006022
dc.identifierhttp://arxiv.org/abs/math/0006022
dc.identifierThe final corrected version of this article appears in the American Journal of Mathematics Volume 123, Issue 3: June, 2001, pages 525-550. Copyright <copyright sign> 2001 by The Johns Hopkins University Press."
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59342
dc.subjectDifferential Geometry
dc.subjectQuantum Algebra
dc.subject17A32, 53C20, 20N05
dc.titleLeibniz Algebras, Courant Algebroids, and Multiplications on Reductive Homogeneous Spaces
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