Hom-Nijienhuis operator and $T$*-extension of Hom-Lie Superalgebras

TL;DR

This paper explores hom-Nijienhuis operators and $T^*$-extensions in hom-Lie superalgebras, demonstrating their properties and implications for algebraic structure preservation and deformation triviality.

Contribution

It introduces the concepts of hom-Nijienhuis operators and $T^*$-extensions for hom-Lie superalgebras, analyzing their properties and equivalence.

Findings

Deformations generated by hom-Nijienhuis operators are trivial.

$T^*$-extensions preserve nilpotency, solvability, and decomposition.

The paper investigates the equivalence of $T^*$-extensions.

Abstract

In this paper, we study hom-Lie superalgebras. We give the definition of hom-Nijienhuis operators of regualr hom-Lie superalgebras and show that the deformation generated by a hom-Nijienhuis operator is trivial. Moreover, we introduce the definition of $T^*$-extensions of Hom-Lie superalgebras and show that $T^*$-extensions preserve many properties such as nilpotency, solvability and decomposition in some sense. We also investigate the equivalence of $T^*$-extensions.