Torsion automorphisms of simple Lie algebras (Q993653)

Let \({\mathfrak g}\) be a simple finite-dimensional complex Lie algebra. An automorphism \(\sigma\) of \({\mathfrak g}\) is called torsion if it has finite order in the group of automorphisms of \({\mathfrak g}\). The classification of such automorphisms is due to [\textit{V. G. Kac}, Infinite-dimensional Lie algebras. Cambridge etc.: Cambridge University Press (1990; Zbl 0716.17022)]. In this paper the author obtains Kac's classification directly from the geometry of the affine Weyl group, without using infinite-dimensional Lie algebras.