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

Published 27 Apr 2013 in math.RA | (1304.7338v1)

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.}