Bihom-Nijienhuis operators and $T^*$-extensions of Bihom-Lie superalgebras

Year 2019, Volume: 48 Issue: 3, 785 - 799, 15.06.2019

Juan Li Liangyun Chen , Bing Sun

Abstract

The purpose of this article is to study Bihom-Nijienhuis operators and $T^*$-extensions of Bihom-Lie superalgebras. We show that the deformation generated by a Bihom-Nijienhuis operator is trivial. Moreover, we introduce the definition of $T^*$-extensions of Bihom-Lie superalgebras and show that $T^*$-extensions preserve many properties such as nilpotency, solvability and decomposition in some sense. In particular, we discuss the equivalence of $T^*$-extensions.

Keywords

Bihom-Lie superalgebras, Bihom-Nijienhuis operators, deformations, $T$*-extensions

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