论文标题
在非阿贝尔张量的谎言广场上的尺寸上
On the dimension of non-abelian tensor square of Lie superalgebras
论文作者
论文摘要
在本文中，我们确定了有限尺寸lie superalgebra的非亚伯张量产物的上限。更确切地说，如果$ l $是dimension $（k \ mid l）$的非阿布莱恩nilpotent Lies lie Allgebra，并且其派生的sibalgebra具有尺寸$（r \中部S）$，则是$ \ dim（l \ otimes l \ otimes l）\ leq（k+l-（r+s）（r+s）（k+l-1）（k+l-1）+2 $ 2 $。我们讨论了平等符合$ r = 1的条件，s = 0 $显式。
In this paper, we determine upper bound for the non-abelian tensor product of finite dimensional Lie superalgebra. More precisely, if $L$ is a non-abelian nilpotent Lie superalgebra of dimension $(k \mid l)$ and its derived subalgebra has dimension $(r \mid s)$, then $ \dim (L\otimes L) \leq (k+l-(r+s))(k+l-1)+2$. We discuss the conditions when the equality holds for $r=1, s=0$ explicitly.
