Non-filiform characteristically nilpotent and complete Lie algebras

In this paper, we construct large families of characteristically nilpotent 4 Lie algebras by considering deformations of the Lie algebra g((m,m-1)(4)) of type Q(n), which arises as a central naturally graded extension of the filiform. Lie algebra L-n. By studying the graded cohomology spaces, we obtain that the sill algebras associ ated to the models g((mm-1))(4) can be interpreted as nilradicals of solvable, complete Lie algebras. For extreme cocycles, we obtain moreover nilradicals of rigid laws. By considering supplementary cocycles, we construct, for any dimension n greater than or equal to 9, non-filiform characteristically nilpotent Lie algebras with mixed characteristic sequence and show that for certain deformations, these deformations are compatible with central extensions. 2000 Mathematics Subject Classification: 171330, 171356.