论文标题
相对自由的有限级代数
Relatively free algebras of finite rank
论文作者
论文摘要
令$ \ mathbb {k} $为特征零的字段，$ b = b_0+b_1 $ a有限维度关联超级级。在本文中，我们研究了由$ b $的格拉斯曼信封定义的品种$ \ mathfrak v $的相对自由代数的多项式身份。我们还考虑了由$ b $，$ g^{（k）}（b）$的$ k $ th Grassmann信封，该信封由$ k $生成的格拉斯曼代数构建，而不是无限的尺寸格拉斯曼代数。我们专门研究代数$ _2（g）$和$ ut_2（g^{（k）}）$的研究，可以将其视为Grassmann信封和$ k $ -th Grassmann Invelope，分别是Superalgebra $ _2（\ Mathbb {k} [k} [k} [k} [u]）$，$ ut_2 $^2 = 2 = 2 = 2 = 2 = 2 = 1 $^2 = 1 $^2 = 1 $^2 = 1 $。
Let $\mathbb{K}$ be a field of characteristic zero and $B=B_0+B_1$ a finite dimensional associative superalgebra. In this paper we investigate the polynomial identities of the relatively free algebras of finite rank of the variety $\mathfrak V$ defined by the Grassmann envelope of $B$. We also consider the $k$-th Grassmann Envelope of $B$, $G^{(k)}(B)$, constructed with the $k$-generated Grassmann algebra, instead of the infinite dimensional Grassmann algebra. We specialize our studies for the algebra $UT_2(G)$ and $UT_2(G^{(k)})$, which can be seen as the Grassmann envelope and $k$-th Grassmann envelope, respectively, of the superalgebra $UT_2(\mathbb{K}[u])$, where $u^2=1$.
