Abstract
Today a few concrete results concerning cohomological calculations on nilpotent Lie algebras are revealed. In this chapter we present these calculations for some particular but nevertheless important classes of nilpotent Lie algebras : i.e. the filiform algebras and the nilradicals of parabolic algebras. We restrict ourselves here to the cohomology whose coefficients are in the adjoint module; some results concerning the cohomology with values in the field are given in the last chapter. As the Lie algebra of derivations related with the first cohomology group, we endeavour to describe this algebra.
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