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- W4288055534 abstract "The main object of study of this paper is the notion of 3-Lie superalgebras with superderivations. We consider a representation $(Phi,mathcal{P})$ of a $3$-Lie superalgebra $mathcal{Q}$ on $mathcal{P}$ and construct first-order cohomologies by using superderivations of $mathcal{P},mathcal{Q}$ which induces a Lie superalgebra $mathcal{T}_{Phi}$ and its representation $Psi$. Then we consider abelian extensions of $3$-Lie superalgebras of the form $0rightarrow mathcal{P}hookrightarrow mathcal{L}rightarrow mathcal{Q}rightarrow 0$ with $[mathcal{P},mathcal{P},mathcal{L}]=0$ and construct an obstruction class to extensibility of a compatible pair of superderivation. Moreover we prove that a pair of superderivation is extensible if and only if its obstruction class is trivial under some suitable conditions." @default.
- W4288055534 created "2022-07-28" @default.
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- W4288055534 date "2022-07-23" @default.
- W4288055534 modified "2023-10-16" @default.
- W4288055534 title "Cohomology, superderivations, and abelian extensions of $3$-Lie superalgebras" @default.
- W4288055534 doi "https://doi.org/10.48550/arxiv.2207.11443" @default.
- W4288055534 hasPublicationYear "2022" @default.
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