The isomorphic realization of nondegenerate solvable Lie algebras of maximal rank based on Kac-Moody algebras (Q1955506)

The paper under review studies finite-dimensional solvable Lie algebras \({\mathcal G}\) over the ground field \({\mathbb C}\), and the nondegeneracy referred to in the title means that \({\mathcal G}\) carries a nondegenerate symmetric bilinear form. One shows how this data under an additional maximal rank hypothesis leads to a generalized Cartan matrix \(A\), hence to a Kac-Moody algebra \({\mathcal G}(A)\), and then the initial algebra \({\mathcal G}\) is realized as a subspace of \({\mathcal G}(A)\).