2 - Kac-Moody algebras

Abstract

For many articles on Kac-Moody algebras and related topics, one can refer Sthanumoorthy and Misra [240]. The real and imaginary roots [25] for Kac-Moody algebras were introduced by Kac [20]. The notion of imaginary roots has no counter part in the finite-dimensional theory. The imaginary roots for affine Kac-Moody Lie algebras had been completely and explicitly described by Kac [8, 21] and their characterization to a certain extent for symmetrizable hyperbolic indefinite Kac-Moody algebras was done by Moody [55]. Kac [56] also introduced the notion of strictly imaginary roots. Moody [17] introduced real roots, called Weyl roots. Casperson [57] gave a complete characterization of Kac-Moody algebras possessing the strictly imaginary property and Bennett [54] has shown the existence of special imaginary roots.