Let \(\mathfrak {g}\) be a complex simple Lie algebra. We consider subalgebras \(\mathfrak {m}\) which are Levi factors of parabolic subalgebras of \(\mathfrak {g}\), or equivalently \(\mathfrak {m}\) is the centralizer of its center. We introduced the notion of admissible systems on finite order \(\mathfrak {g}\)-automorphisms 𝜃, and show that 𝜃 has admissible systems if and only if its fixed point set is a Levi factor. We then use the extended Dynkin diagrams to characterize such automorphisms, and look for automorphisms of minimal order.

中文翻译：

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利维因子和可容许的同构

令\（\ mathfrak {g} \）是一个复杂的简单李代数。我们认为子代数\（\ mathfrak {m} \）是\（\ mathfrak {g} \）抛物子代数的Levi因子，或者等效地\（\ mathfrak {m} \）是其中心的中心点。我们介绍受理系统的有限顺序的概念\（\ mathfrak {G} \） -automorphisms θ，并表明，θ具有受理系统当且仅当其固定点集是一列维因素。然后，我们使用扩展的Dynkin图来刻画这种自同构，并寻找最小阶的自同构。