Cohomologically rigid solvable Lie algebras with a nilradical of arbitrary characteristic sequence

It is shown that for a finite-dimensional solvable rigid Lie algebra rr, its rank is upper bounded by the length of the characteristic sequence c(n)c(n) of its nilradical nn. For any characteristic sequence c=(n1,⋯,nk,1)c=(n1,⋯,nk,1), it is proved that there exists at least a solvable Lie algebra rcrc the nilradical of which has this characteristic sequence and that satisfies the conditions Hp(rc,rc)=0Hp(rc,rc)=0 for p≤3p≤3.