On the Lie triple derivation of Hom–Lie superalgebras

Abstract

Consider a Hom–Lie superalgebra, denoted by [Formula: see text]. In this paper, we inquire the Lie triple derivation [Formula: see text] and generalized Lie triple derivation [Formula: see text] of Hom–Lie superalgebra. Later, we address the triple centroid, triple quasi-centroid and central triple derivations of Hom–Lie superalgebra. Moreover, we attempt to show the relationship of triple centroid, triple quasi-centroid and central triple derivation with [Formula: see text] and [Formula: see text]. We give complete classification of triple derivations of Hom–Lie superalgebra, where we show that for the simple Hom–Lie superalgebras [Formula: see text].