Maximal subalgebras for Lie superalgebras of Cartan type

Abstract

The maximal graded subalgebras for four families of Lie superalgebras of Cartan type over a field of prime characteristic are studied. All maximal graded subalgebras are described completely by a constructive method and their isomorphism classes, dimension formulas are found except for maximal irreducible graded subalgebras. The classification of maximal irreducible graded subalgebras is reduced to the classification of the maximal irreducible subalgebras for the classical Lie superalgebras 𝔤𝔩(m, n), 𝔰𝔩(m, n) and 𝔬𝔰𝔭(m, n).