K2 of Kac-Moody groups

Ulf Rehmann and Jun Morita, in their 1989 paper A Matsumoto Type Theorem for Kac-Moody Groups, gave a presentation of K2(A,F) for any generalised Cartan matrix A and field F. The purpose of this paper is to use this presentation to compute K2(A,F) more explicitly in the case when A is hyperbolic. In particular, we shall show that these K2(A,F) can always be expressed as a product of quotients of K2(F) and K2(2,F). Along the way, we shall also prove a similar result in the case when A has an odd entry in each column.