论文标题
$ 3 $ -Lie Superalgebras的同时，倾斜和Abelian Extensions
Cohomology, superderivations, and abelian extensions of $3$-Lie superalgebras
论文作者
论文摘要
本文研究的主要对象是具有倾斜度的3-lie超级乳房的概念。我们考虑一个表示$ 3 $ -LIE SUPERALGEBRA $ \ MATHCAL {Q} $的表示$（φ，\ Mathcal {p}）$在$ \ Mathcal {p} $上和构造一阶共同体上，并使用$ \ Mathcal {p}，\ Mathcal a liela的uctergr { $ \ MATHCAL {T}_φ$及其表示$ψ$。然后，我们考虑表格$ 0 \ rightarrow \ mathcal {p} \ hookrightArrow \ Mathcal {l} \ rightArrow \ rightarrow \ Mathcal {q} \ rightarrow 0 $ with $ [\ nathcal {p} p}，lakecal {并构建一个障碍物，以使兼容的一对脱落的可扩展性。此外，我们证明，只有在某些合适的条件下，且仅当其阻塞类是微不足道的时，就可以扩展一对脱落。
The main object of study of this paper is the notion of 3-Lie superalgebras with superderivations. We consider a representation $(Φ,\mathcal{P})$ 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 $\mathcal{T}_Φ$ and its representation $Ψ$. Then we consider abelian extensions of $3$-Lie superalgebras of the form $0\rightarrow \mathcal{P}\hookrightarrow \mathcal{L}\rightarrow \mathcal{Q}\rightarrow 0$ 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.
