  In this paper, we study 3-Lie algebras with derivations. We call the pair
consisting of a 3-Lie algebra and a distinguished derivation by the 3-LieDer
pair. We define a cohomology theory for 3-LieDer pair with coefficients in a
representation. We study central extensions of a 3-LieDer pair and show that
central extensions are classified by the second cohomology of the 3-LieDer pair
with coefficients in the trivial representation. We generalize Gerstenhaber's
formal deformation theory to 3-LieDer pairs in which we deform both the 3-Lie
bracket and the distinguished derivation.
