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

TL;DR

This paper investigates the properties of complete hom-Lie superalgebras, establishing conditions for their completeness and simplicity, and exploring their decomposition and derivation structures.

Contribution

It introduces new criteria for completeness and simplicity in hom-Lie superalgebras and analyzes their decomposition and derivation properties.

Findings

Established equivalent conditions for completeness

Described the relation between decomposition and completeness

Identified conditions for the set of α^s-derivations to be complete

Abstract

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.