Root multiplicities of some generalized Kac-Moody algebras
In 1988, Borcherds introduced the notion of generalized Kac-Moody algebras. Later, the authors of this paper studied them and gave in different papers some properties of these algebras. Indeed, they extended the notion of purely imaginary roots of Kac-Moody algebras to them and classified all of generalized Kac-Moody algebras having purely imaginary property. Among these last algebras, they also found those whose purely imaginary roots are strictly imaginary, giving also complete classifications of generalized Kac-Moody algebras having special imaginary roots and strictly imaginary property. In this paper, the authors continue with this research by determining explicitly the root multiplicities of all roots of generalized Kac-Moody algebras associated with Borcherds-Cartan matrices (of order 3)which are extensions of finite \(A_3\), affine \(A_2^{(1)}\) and hyperbolic \(HA_1\), and they also compute the root multiplicities of some generalized Kac-Moody algebras with more than one imaginary simple root.
scientific article; zbMATH DE number 5186301