Simply complete hom-Lie superalgebras and decomposition of complete hom-Lie superalgebras

Abstract

In this paper, we study some equivalent conditions for a hom-Lie superalgebra to be a complete hom-Lie superalgebra. In particular, we discuss the relationship between decomposition and completness for a hom-Lie superalgebra. Moreover, we check some conditions that the set of α s -derivations of a hom-Lie superalgebra to be complete and simply complete.