On split involutive regular BiHom-Lie superalgebras
This paper under review is concerned with an abstract superalgebraic structure (called \text{split involutive regular BiHom-Lie superalgebras}) that generalizes two kinds of important algebras: split involutive regular Hom-Lie algebras and split regular BiHom-Lie superalgebras. Using some techniques analogous to those appeared in the theory of semisimple Lie algebras and Lie superalgebras, the authors explore several structure theorems of such superalgebras. The authors prove that any ideal of a perfect split involutive regular BiHom-Lie superalgebra that has maximal length and satisfies root-multiplicativity is involutive, as well as characterize simple perfect split involutive regular BiHom-Lie superalgebras with maximal length and root-multiplicativity by an equivalence relation. Finally, the authors prove that any perfect split involutive regular BiHom-Lie superalgebra with maximal length and root-multiplicativity is a direct sum of simple involutive ideals, where each of these ideals has all its roots connected.
scientific article; zbMATH DE number 7435370
scientific article