Root systems arising from automorphisms

Abstract

We study a combinatorial approach of producing new root systems from the old ones in the context of affine root systems and their new generalizations. The appearance of this approach in the literature goes back to the outstanding work of Kac in the realization of affine KacMoody Lie algebras. In recent years, this approach has been appeared in many other works, including the study of affinization of extended affine Lie algebras and invariant affine reflection algebras. © 2012 World Scientific Publishing Company.