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 K 2 ( A , F ) for any generalised Cartan matrix A and field F . The purpose of this paper is to use this presentation to compute K 2 ( A , F ) more explicitly in the case when A is hyperbolic. In particular, we shall show that these K 2 ( A , F ) can always be expressed as a product of quotients of K 2 ( F ) and K 2 ( 2 , F ) . Along the way, we shall also prove a similar result in the case when A has an odd entry in each column. [ABSTRACT FROM AUTHOR]