论文标题
在$ n $ -Slice代数和相关代数上
On $n$-slice Algebras and Related Algebras
论文作者
论文摘要
$ n $ -Slice代数作为较高维表示理论中的路径代数的概括。在本文中，我们通过其$（n+1）$ - 预注射式代数和其二次二重奏的琐碎扩展来提供$ n $ -Slice代数的分类。一个人总是可以将tame $ n $ -slice代数与$ \ mathrm {gl}的有限子组的mckay颤抖联系起来（n+1，\ mathbb c）$。在$ n = 2 $的情况下，我们描述了与$ 2 $ -Slice代数的关系，与有限的Abelian子组的McKay Quiver相关的$ \ MATHRM {SLRM {SL}（3，\ Mathbb c）$以及从嵌入$ \ MATHRM {$ \ MATHRM {2，$ {2，\ bb c C）获得的有限亚组$ \ mathrm {sl}（3，\ mathbb c）$。
The $n$-slice algebra is introduced as a generalization of path algebra in higher dimensional representation theory. In this paper, we give a classification of $n$-slice algebras via their $(n+1)$-preprojective algebras and the trivial extensions of their quadratic duals. One can always relate tame $n$-slice algebras to the McKay quiver of a finite subgroup of $\mathrm{GL}(n+1, \mathbb C)$. In the case of $n=2$, we describe the relations for the $2$-slice algebras related to the McKay quiver of finite Abelian subgroups of $\mathrm{SL}(3, \mathbb C)$ and of the finite subgroups obtained from embedding $\mathrm{SL}(2, \mathbb C)$ into $\mathrm{SL}(3,\mathbb C)$.
