Some properties of modules for generalized Kac-Moody algebras (Q1309124)

Let \(g(A)\) be a generalized Kac-Moody algebra associated with a real \(n\times n\) matrix \(A= (a_{ij})\) satisfying the following properties: (i) either \(a_{ii} =2\) or \(a_{ii}\leq 0\); (ii) \(a_{ij}\leq 0\) if \(i\neq j\), and \(a_{ij}\in \mathbb{Z}\) if \(a_{ii}=2\); (iii) \(a_{ij}=0\) implies \(a_{ji}=0\). Several properties of integrable (highest weight) modules are proved.