3 - Generalized Kac-Moody algebras

Abstract

Borcherds initiated the study of generalized Kac-Moody (GKM) algebras [27, 95, 96]. For automorphism of GKM algebras, one can refer Fuchs et al. [97]. In Kac-Moody algebras all simple roots are real whereas in the GKM algebras, one can have imaginary simple roots with norms > 0 and multiplicities > 1 [37]. The concept of special imaginary roots was extended from Kac-Moody algebras to GKM algebras in Li et al. [98] and therein they found out a special imaginary root for a particular GKM algebra. Barwald and Gebert [99] presented the results of some calculations of the multiplicities of simple imaginary roots for a particular Borcherds superalgebra and its maximal Kac-Moody subalgebra.