On the structure of split regular -Hom-Jordan-Lie superalgebras

In this paper we study the structure of arbitrary split regular -Hom-Jordan-Lie super algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular -Hom-Jordan-Lie superalgebra L is of the form L = H []   Σ []2= V []; with H  [] a graded linear subspace of the graded abelian subalgebra H and any V [ ]; a well-described ideal of L; satisfying [V [ ]; V []] = 0 if [] ̸= []: Under certain conditions, in the case of L being of maximal length, the simplicity of the algebra is characterized and it is shown that L is the direct sum of the family of its minimal ideals, each one being a simple split regular -Hom-Jordan-Lie superalgebra.