Courant brackets on noncommutative algebras and omni-Lie algebras
arXiv:math/0604101
Abstract
We define a Courant bracket on an associative algebra using the theory of Hochschild homology, and we introduce the notion of Dirac algebra. We show that the bracket of an omni-Lie algebra is quite a kind of Courant bracket.
18pages,Tokyo Journal of Mathematics (to appear)