Solvabilizers of Lie algebras of Cartan type

Determine the solvabilizer sol(L) for finite-dimensional Lie algebras of Cartan type, thereby resolving the open problem concerning the structure of sol(L) in this class.

Background

The paper identifies the solvable radical R(L) with sol(L) under hypotheses including an infinite base field of characteristic greater than 3 and a classical semisimple quotient L/R(L). It then explicitly notes that the corresponding question for Lie algebras of Cartan type remains unresolved. This problem is included because it asks for an extension of the solvabilizer–radical characterization beyond the classes covered by the preceding theorem.