论文标题
$ {\ mathbb z} _2 $ - 免费的Jordan Superalgebra $ J（d_1 | d_2）$的尺寸
The ${\mathbb Z}_2$-graded dimensions of the free Jordan superalgebra $J(D_1|D_2)$
论文作者
论文摘要
令$ k $为特征$ 0 $的字段。对于superspace $ v = v_ \ bar {0} \ oplus v_ \ bar {1} $上的$ k $，我们称为vector $（\ dim_k v_ v_ v_ \ bar {0}，\ dim_k v_k v_ \ bar v_ \ bar {1}）令$ j（d_1 | d_2）$是由$ d_1 $甚至发电机和$ d_2 $奇数生成器生成的免费Jordan Superalgebra。在本文中，我们研究了$ j（d_1 | d_2）$的$ n $组件的分级维度，并找到它们与$ j（d_1 | d_2）$的tits-allison-gao的同源性，遵循i.kashuba and o..mathieu在[kmathieu in [kmathieu in [kmathie''的方法中，他们与他们在哪里免费JORD JORD jORD JORD。并且，我们的论文提出了上述内容的四个有趣的猜想。
Let $k$ be a field of characteristic $0$. For a superspace $V=V_\bar{0}\oplus V_\bar{1}$ over $k$, we call the vector $(\dim_k V_\bar{0} ,\dim_k V_\bar{1})$ the (${\mathbb Z}_2$-)graded dimension of $V$. Let $J(D_1|D_2)$ be the free Jordan superalgebra generated by $D_1$ even generators and $D_2$ odd generators. In this paper, we study the graded dimensions of the $n$-components of $J(D_1|D_2)$ and find the connection between them and the homology of Tits-Allison-Gao Lie superalgebra of $J(D_1|D_2)$ following the method given by I.Kashuba and O.Mathieu in [KM], where they deal with the free Jordan algebra. And, four interesting conjectures of above contents are proposed in our paper.
