The Double Field Theory (DFT) is formulated on a certain class of a metric algebroid,
where the structure functions satisfy the
pre-Bianchi identity.
The derived bracket formulation of the metric algebroid by the Dirac generating operator is applied.
The action is formulated by a projected generalized Lichnerowicz formula which is a generalization of the analogous formulation in gravity and supergravity. The flux of the dilaton in this setting is introduced via an ambiguity in the Dirac generating operator, while the dilaton is introduced
via an ambiguity of the divergence on the metric algebroid. This talk is based on [1].