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. Since their independent introduction by Kac [2], [3] and Moody [8],[9] there has been increasing interest in the Generalized Cartan Matrix (GCM) Liealgebras because of their connections with other parts of mathematics (see [4]). Forinstance, the Macdonald identities [7] were shown to be the "denominatorformula" for the Euclidean GCM Lie algebras [3], [10]. We are concerned here withan algebra which falls into the class of algebras called "hyperbolic", whose rootsystems were studied by Moody in [11]. An exciting connection was recently foundby Lepowsky and Moody in [6] between the rank 2 hyperbolic GCM Lie algebrasand Hubert modular surfaces with respect to a real quadratic field. For one ofthese algebras the quadratic field is Q(Vs ). In this paper we show that theFibonacci numbers are intimately related to this algebra by using them to expressthe Weyl-Macdonald-Kac denominator formula (§2). We do not compute the rootmultiplicities, but see §3.1. Preliminaries. The following preliminaries may be found in [6]. A 2 X 2integral matrix (aiy) of the form

A hyperbolic GCM Lie algebra and the Fibonacci numbers