Deformations of Lie 2-algebras

In this paper, we consider deformations of Lie 2-algebras via the cohomology theory. We prove that a 1-parameter infinitesimal deformation of a Lie 2-algebra gg corresponds to a 2-cocycle of gg with the coefficients in the adjoint representation. A Nijenhuis operator on a Lie 2-algebra is introduced to describe trivial deformations. We also study abelian extensions of Lie 2-algebras from the viewpoint of deformations of semidirect product Lie 2-algebras.