论文标题
一个简单的矩阵谎言组及其谎言代数的脱节
Disjointness of a simple matrix Lie group and its Lie algebra
论文作者
论文摘要
令$ g $为$ \ mathrm {gl} _n（\ mathbb {c}）$的连接的封闭子组，它作为谎言组很简单，并且在$ \ mathbb {c}^n $上行为不可总体。关于$ g $及其Lie代数$ \ Mathfrak {G} $作为$ M_N（\ Mathbb {C}）$的子集，我们有$ g \ cap \ mathfrak {g} \ neq \ neq \ emberySet $，并且仅当$ g $是经典的群体和$ \ m m i \ mathbb {c}^n $ a minal of g $ g $时。
Let $G$ be a connected closed subgroup of $\mathrm{GL}_n(\mathbb{C})$ which is simple as a Lie group and which acts irreducibly on $\mathbb{C}^n$. Regarding both $G$ and its Lie algebra $\mathfrak{g}$ as subsets of $M_n(\mathbb{C})$, we have $G\cap \mathfrak{g}\neq\emptyset$ if and only if $G$ is a classical group and $\mathbb{C}^n$ is a minuscule representation.
