Maximal rank root subsystems of hyperbolic root systems

Abstract

A Kac-Moody algebra is called hyperbolic if it corresponds to a generalized Cartan matrix of hyperbolic type. We study root subsystems of root systems of hyperbolic algebras. In this paper, we classify maximal rank regular hyperbolic subalgebras of hyperbolic Kac-Moody algebras.Comment: 16 pages, 19 figures, 1 tabl