A presentation of toroidal algebras a homomorphic images of G.I.M. algebras

Abstract

Let A [1] be a 1-fold affinization of a generalized Cartan matrix A of finite or affine type so that A [1] has two identical columns and two identical rows. We consider a presentation of a toroidal Lie algebra as a homomorphic image of the generalized intersection matrix Lie algebra of A [1] and thus obtain an explicit description of the generators of the kernel from the defining relations