Cohomological rigidity of solvable Lie algebras of maximal rank

The main goal of this talk is to study the cohomological rigidity of solvable Lie algebras of maximal rank. We present several sufficient conditions for the vanishing of the second cohomology group, and we also discuss results concerning the vanishing of higher-order cohomology groups. Moreover, we provide sufficient conditions for the non-rigidity of solvable Lie algebras of maximal rank.