论文标题
特殊线性组的真实伴随轨道
Real adjoint orbits of special linear groups
论文作者
论文摘要
令$ g $为谎言组，lie代数$ \ mathfrak {g} $。一个元素$ x \ in \ mathfrak {g} $称为$ \ mathrm {ad} _g $ -real，如果$ -x = gxg^{ - 1} $，对于某些$ g \ in G $。此外，如果$ -x = gxg^{ - 1} $在g $中持有$ g \，则$ x $被称为强烈$ \ mathrm {ad} _g $ -real。我们已经对$ \ mathrm {ad} _g $ -real和强烈的$ \ mathrm {ad} _g $ - real orbits中的特殊线性lie代数$ \ mathfrak {slfrak {sl}（n，n，n，\ mathbb {f}）$ $ \ mathbb {h} $。
Let $ G $ be a Lie group with Lie algebra $ \mathfrak{g} $. An element $ X \in \mathfrak{g} $ is called $\mathrm{Ad}_G$-real if $ -X=gXg^{-1} $ for some $ g \in G $. Moreover, if $ -X=gXg^{-1} $ holds for some involution $ g\in G $, then $ X $ is called strongly $\mathrm{Ad}_G$-real. We have classified the $\mathrm{Ad}_G$-real and the strongly $\mathrm{Ad}_G$-real orbits in the special linear Lie algebra $\mathfrak{sl}(n,\mathbb{F}) $ for $ \mathbb{F}=\mathbb{C}$ or $\mathbb{H} $.
