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

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

2000-06-04

arxiv.org/abs/math/0006022v2

The final corrected version of this article appears in the American Journal of Mathematics Volume 123, Issue 3: June, 2001, pa

Mathematics

Differential Geometry

24 pages. Version 2 has minor corrections

Scientific paper

We 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.

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