论文标题
$ n $ -lie Superalgebra的Schur乘数
The Schur multiplier of an $n$-Lie superalgebra
论文作者
论文摘要
在本文中，我们研究了$ n $ -lie superalgebra $ l $的Schur乘数$ \ Mathcal $ \ Mathcal {M}（L）$，并证明$ \ dim \ dimcal {m {m}（l）（l）\ leq \ leq \ sum___ \ Mathcal {l}（n-i，k）$，其中$ \ dim l =（m | k）$，$ \ nathcal {l}（0，k）= 1 $和$ \ Mathcal {l}（t，t，k）= \ sum_ = \ sum_ {j = 1} $ 1 \ leq t \ leq n $。此外，我们获得了$ \ Mathcal {m}（l）$的尺寸的上限，其中$ l $是具有一维派生的Superalgebra的nilpotent $ n $ -lie-lie Superalgebra。还提供了$ \ dim \ dim \ Mathcal {m}（l）$的几种不等式，以及$ n $ -lie-lie superalgebra类似物的相反。
In the present paper, we study the notion of the Schur multiplier $\mathcal{M}(L)$ of an $n$-Lie superalgebra $L$, and prove that $\dim \mathcal{M}(L) \leq \sum_{i=0}^{n} {m\choose{i}} \mathcal{L}(n-i,k)$, where $\dim L=(m|k)$, $\mathcal{L}(0,k)=1$ and $\mathcal{L}(t,k) = \sum_{j=1}^{t}{{t-1}\choose{j-1}} {k\choose j}$, for $1\leq t\leq n$. Moreover, we obtain an upper bound for the dimension of $\mathcal{M}(L)$ in which $L$ is a nilpotent $n$-Lie superalgebra with one-dimensional derived superalgebra. It is also provided several inequalities on $\dim\mathcal{M}(L)$ as well as an $n$-Lie superalgebra analogue of the converse of Schur's theorem.
