论文标题
在概括的海森堡的三重张量产品上，排名$ \ leq2 $
On the triple tensor product of generalized Heisenberg Lie superalgebra of rank $\leq2$
论文作者
论文摘要
在本文中，我们计算了所有广义海森堡的Schur乘数，排名$ 2 $。我们讨论$ \ otimes^3h $和$ \ wedge^3h $的结构，其中$ h $是概括的Heisenberg Lie Superalgebra，属于$ \ leq2 $。此外，我们证明，如果$ l $是$（m \ mid n）$ - 尺寸非亚伯式nilpotent lie superalgebra，则具有dimension $（r \ mid s）$的subalgebra，则是$ \ \ dim \ otimes^3l^3l \ leq（m+n）（m+n-（m+n-（m+s））^2 $。特别是，对于$ r = 1，s = 0 $，当时仅当$ l \ cong h（1 \ mid 0）$时，相等性。
In this article, we compute the Schur multiplier of all generalized Heisenberg Lie superalgebras of rank $2$. We discuss the structure of $\otimes^3H$ and $\wedge^3H$ where $H$ is a generalized Heisenberg Lie superalgebra of rank $\leq2$. Moreover, we prove that if $L$ is an $(m\mid n)$-dimensional non-abelian nilpotent Lie superalgebra with derived subalgebra of dimension $(r\mid s)$, then $\dim\otimes^3L \leq (m+n)(m+n - (r+s))^2$. In particular, for $r=1,s=0$ the equality holds if and only if $L \cong H(1\mid 0)$.
