Simply Complete Hom-Lie Superalgebras and Decomposition of Complete Hom-Lie Superalgebras

Abstract

Complete hom-Lie superalgebras 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 linear space of $$\alpha ^{s}$$ α s -derivations of a hom-Lie superalgebra to be complete and simply complete are obtained.