Canadian mathematical bulletin | |
Some Questions about Semisimple Lie Groups Originating in Matrix Theory | |
关键词: Jacobian Conjecture; injectivity; Monge--Ampère equation; | |
DOI : 10.4153/CMB-2003-035-1 | |
学科分类:数学(综合) | |
来源: University of Toronto Press * Journals Division | |
【 摘 要 】
We generalize the well-known result that a square traceless complexmatrix is unitarily similar to a matrix with zero diagonal toarbitrary connected semisimple complex Lie groups $G$ and their Liealgebras $mathfrak{g}$ under the action of a maximal compact subgroup$K$ of $G$. We also introduce a natural partial order on$mathfrak{g}$: $xle y$ if $f(Kcdot x) subseteq f(Kcdot y)$ forall $fin mathfrak{g}^*$, the complex dual of $mathfrak{g}$. Thispartial order is $K$-invariant and induces a partial order on theorbit space $mathfrak{g}/K$. We prove that, under some restrictionson $mathfrak{g}$, the set $f(Kcdot x)$ is star-shaped with respectto the origin.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912050576310ZK.pdf | 36KB | download |