Solvabilizer characterization for Lie algebras of Caratan type

Determine the solvabilizer sol(L) for finite-dimensional Lie algebras of Caratan type, and characterize its relationship with the solvable radical.

Background

The paper proves that, under specified hypotheses in positive characteristic, the solvabilizer sol(L) coincides with the solvable radical R(L), extending a characteristic-zero result. It then identifies the determination of sol(L) for Lie algebras of Caratan type as an unresolved case. The problem concerns whether an analogous radical characterization holds in that setting.

References

Investigating $sol(L)$ when $L$ is of Caratan type remains an open problem.

— The solvable Graph of a finite-dimensional Lie Algebra  (2511.08290 - Towers et al., 11 Nov 2025) in Section 3, subsection “The solvabilizer of a Lie algebra”