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

Michael K. Kinyon·Alan Weinstein
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Abstract

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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BibTeXRIS

Michael K. Kinyon, Alan Weinstein. 2000-07-06. Leibniz Algebras, Courant Algebroids, and Multiplications on Reductive Homogeneous Spaces. https://arxiv.org/abs/math/0006022

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