Infinitesimal Symmetries of Dixmier-Douady Gerbes

We introduce the infinitesimal symmetries of Dixmier-Douady gerbes over a manifold M, both with and without connective structures and curvings. We explore the algebraic structure possessed by these symmetries, and relate them to equivariant gerbes via a "differentiation functor". In the case that a gerbe G is equipped with a connective structure A, we give a new construction of the Courant algebroid associated to (G,A) directly in terms of the infinitesimal symmetries of (G,A).