特殊线性群的拓扑生成
Topological generation of special linear groups
摘要：
设$C_1,\ldots,C_e$是定义在一个充分大的域$k$上的代数群$G=SL_n(k)$的非中心共轭类，设$Ω:=C_1\times \ldots \times C_e$ .本文给出了在$G$中存在元组$(x_1,\ldots,x_e)\inΩ$使得$\langle x_1,\ldots,x_e\rangle$是Zerkiki稠密的充要条件.因此，证明了代数群线性表示的一般稳定子的一个新结果，加强了李型有限群的随机$(r,s)$ -生成的已有结果.
英文摘要：
Let $C_1,\ldots,C_e$ be noncentral conjugacy classes of the algebraic group $G=SL_n(k)$ defined over a sufficiently large field $k$, and let $Ω:=C_1\times \ldots \times C_e$. This paper determines necessary and sufficient conditions for the existence of a tuple $(x_1,\ldots,x_e)\inΩ$ such that $\langle x_1,\ldots,x_e\rangle$ is Zariski dense in $G$. As a consequence, a new result concerning generic stabilizers in linear representations of algebraic groups is proved, and existing results on random $(r,s)$-generation of finite groups of Lie type are strengthened.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
