Leibniz algebras, Courant algebroids, and multiplications on reductive homogeneous spaces

Citation
Mk. Kinyon et A. Weinstein, Leibniz algebras, Courant algebroids, and multiplications on reductive homogeneous spaces, AM J MATH, 123(3), 2001, pp. 525-550
Citations number
22
Categorie Soggetti
Mathematics
Journal title
AMERICAN JOURNAL OF MATHEMATICS
ISSN journal
00029327 → ACNP
Volume
123
Issue
3
Year of publication
2001
Pages
525 - 550
Database
ISI
SICI code
0002-9327(200106)123:3<525:LACAAM>2.0.ZU;2-Z
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 section s of Courant algebroids and on the "omni-Lie algebras" recently introduced by the second author.