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

Complete hom-Lie superalgebra are considered and some equivalent conditions for a hom-Lie superalgebra to be a complete hom-Lie superalgebra are established. In particular, the relation between decomposition and completeness for a hom-Lie superalgebra is described. Moreover, some conditions that the set of \(\alpha^{s}\)-derivations of a hom-Lie superalgebra to be complete and simply complete are obtained.