K 2 of Kac–Moody groups

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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
Original languageEnglish
JournalJournal of Algebra
Publication statusPublished - Aug 2017


  • Kac-Moody Groups
  • Matsumoto’s Theorem
  • K_2(A, F)
  • K-Theory


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