Levi Factors and Admissible Automorphisms

Abstract

Listen

Translate article

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 \U0001d703, and show that \U0001d703 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.