Duality construction of symmetrizable Kac-Moody algebras

We know that there is a one to one correspondence between Kac-Moody algebra s and generalized Cartan matrices. In Kac ("Infinite-Dimensional Lie algebr as," 3rd ed., Cambridge Univ. Press, Cambridge, UK, 1990), one can find a w ay to reconstruct such an algebra as a Lie algebra presented by generators and relations. The aim of the present work is to give another way to recons truct those algebras when the Cartan matrix is symmetrisable. Our method wi ll use a semi-classical version of techniques of quantum groups. (C) 1999 A cademic Press.