论文标题
$ \ mathsf a_ \ ell $ -commutator关系的组
Groups with $\mathsf A_\ell$-commutator relations
论文作者
论文摘要
如果$ a $是一个Unital Associative戒指，$ \ ell \ geq 2 $，则通用线性组$ \ mathrm {gl}（\ ell，a）$具有root subgroups $u_α$和weyl elements $n_α$ for $n_α$ for $n_α$ for $α$ for for Type $ \ alssf a _ _ _ _ a _ _ _ e _ el _ ell -ell -ell -ell -1}的根系。相反，如果一个任意组的根子组和Weyl元素，则适用于满足自然条件的$ \ ell \ geq 4 $，那么有一种方法可以恢复戒指$ a $。我们证明了该结果不使用Weyl元素的概括，因此，我们不是矩阵环$ \ mathrm m（\ ell，a）$，我们构建了一个具有良好行为的Peirce分解的非非大学关联环。
If $A$ is a unital associative ring and $\ell \geq 2$, then the general linear group $\mathrm{GL}(\ell, A)$ has root subgroups $U_α$ and Weyl elements $n_α$ for $α$ from the root system of type $\mathsf A_{\ell - 1}$. Conversely, if an arbitrary group has such root subgroups and Weyl elements for $\ell \geq 4$ satisfying natural conditions, then there is a way to recover the ring $A$. We prove a generalization of this result not using the Weyl elements, so instead of the matrix ring $\mathrm M(\ell, A)$ we construct a non-unital associative ring with a well-behaved Peirce decomposition.
