Classification of finite-dimensional simple modular Lie superalgebras

Determine a complete classification of finite-dimensional simple modular Lie superalgebras.

Background

The paper studies skew-symmetric super-biderivations of the special odd Hamiltonian Lie superalgebra SHO(n,n; t) over a field of characteristic p > 2, proving that all such super-biderivations are inner. In setting the broader context, the authors note that while the theory over characteristic zero is well developed, the modular (positive characteristic) case is less complete.

They highlight a central gap in the field: despite substantial progress on structures, derivations, and representations for the eight families of finite-dimensional Cartan-type modular Lie superalgebras (W, S, H, K, HO, KO, SHO, SKO), a full classification of all finite-dimensional simple modular Lie superalgebras has not been achieved.