The semidirect product of a Lie algebra and a 2-term representation up to
homotopy is a Lie 2-algebra. Such Lie 2-algebras include many examples arising
from the Courant algebroid appearing in generalized complex geometry. In this
paper, we integrate such a Lie 2-algebra to a strict Lie 2-group in the finite
dimensional case.Comment: 31 pages, no figure, Int. J. Geom. Methods Mod. Phys. Vol. 9, No. 5
(2012) 1250043. DOI No: 10.1142/S0219887812500430 125004
