Maximal non-graded subalgebras

Classify the maximal non-graded subalgebras of the three exceptional simple Lie superalgebras \mathfrak{osp}_a(4|2), \mathfrak{ag}(2), and \mathfrak{ab}(3), removing the restriction to graded subalgebras.

Background

The paper solves the maximal-subalgebra problem only for graded subalgebras relative to the selected Weisfeiler gradings. Its lists include maximal graded subalgebras and, in cases certified by the torus criterion, maximal subalgebras of the ambient Lie superalgebra.

The complete classification without a grading restriction is not provided. Because the three exceptional Lie superalgebras are finite-dimensional, the authors describe this unresolved extension as a finite problem.

References

Describe the maximal non-graded subalgebras of the three exceptions, i.e., drop the restriction to graded subalgebras imposed in the formulation PROB.

— Maximal subalgebras in the three exceptional simple finite-dimensional Lie superalgebras  (2610.03354 - Leites et al., 2 Oct 2026) in Section 8, Problem \ref{Pnongraded}, “The maximal non-graded subalgebras”