Deformed Kac-Moody algebras and their representations
For any generalized Cartan matrix \(A\), the authors introduced the Lie algebra \(\mathfrak{G}(A)\). This algebra, a generalization of nondegenerate Lie algebras was investigated by many other authors recently, and can also be regarded as a certain deformation of Kac-Moody algebras. Therefore, similar methods can be used to study the structure and representation theory of this algebra. In the present paper, the lowest weight modules and the highest weight modules are described, and some better results are obtained in the case of the symmetrizable \(A\).
scientific article; zbMATH DE number 5304630