Levi Factors and Admissible Automorphisms

Abstract

AbstractLet $\mathfrak {g}$ g be a complex simple Lie algebra. We consider subalgebras $\mathfrak {m}$ m which are Levi factors of parabolic subalgebras of $\mathfrak {g}$ g , or equivalently $\mathfrak {m}$ m is the centralizer of its center. We introduced the notion of admissible systems on finite order $\mathfrak {g}$ 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.