2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111452We 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)Symplectic Geometry53D17; 16E40text