location:  Publications → journals
Search results

Search: MSC category 22E60 ( Lie algebras of Lie groups {For the algebraic theory of Lie algebras, see 17Bxx} )

 Expand all        Collapse all Results 1 - 1 of 1

1. CMB 2003 (vol 46 pp. 332)

Đoković, Dragomir Z.; Tam, Tin-Yau
 Some Questions about Semisimple Lie Groups Originating in Matrix Theory We generalize the well-known result that a square traceless complex matrix is unitarily similar to a matrix with zero diagonal to arbitrary connected semisimple complex Lie groups $G$ and their Lie algebras $\mathfrak{g}$ under the action of a maximal compact subgroup $K$ of $G$. We also introduce a natural partial order on $\mathfrak{g}$: $x\le y$ if $f(K\cdot x) \subseteq f(K\cdot y)$ for all $f\in \mathfrak{g}^*$, the complex dual of $\mathfrak{g}$. This partial order is $K$-invariant and induces a partial order on the orbit space $\mathfrak{g}/K$. We prove that, under some restrictions on $\mathfrak{g}$, the set $f(K\cdot x)$ is star-shaped with respect to the origin. Categories:15A45, 20G20, 22E60
 top of page | contact us | privacy | site map |