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

It is shown that for a finite-dimensional solvable rigid Lie algebra r, its rank is upper bounded by the length of the characteristic sequence c(n) of its nilradical n. For any characteristic sequence c = (n(1),..., n(k,) 1), it is proved that there exists at least a solvable Lie algebra re the nilradical of which has this characteristic sequence and that satisfies the conditions H-p (r(c), r(c)) = 0 for p <= 3. (C) 2015 Elsevier Inc. All rights reserved.