The deformation theory of a Dirac structure is controlled by a differential graded Lie algebra
that depends on the choice of an auxiliary transversal Dirac structure; if the transversal is not
involutive, one obtains an algebra instead. We develop a simplified method for describing
this algebra and use it to prove that the algebras corresponding to different transversals are
canonically–isomorphic. In some cases, this isomorphism provides a formality map, as we
show in several examples including (quasi)-Poisson geometry, Dirac structures on Lie …