Lie algebras graded by finite root systems and intersection matrix algebras

摘要

This paper classifies the Lie algebras graded by doubly-laced finite root systems and applies this classification to identify the intersection matrix algebras arising from multiply affinized Cartan matrices of types B, C,F, and' G, This Completes this determination of the Lie algebras graded by finite toot systems initiated by Berman and Moody who studied the imply-laced finite root systerns of rank>2.