This article constructs a crossed module corresponding to the generator of
the third cohomology group with trivial coefficients of a complex simple Lie
algebra. This generator reads as , constructed from the Lie bracket [,]
and the Killing form . The construction is inspired by the corresponding
construction for the Lie algebra of formal vector fields in one formal variable
on R, and its subalgebra sl_2(R), where the generator is usually called
Godbillon-Vey class.Comment: 24 page
