K₂ of Kac-Moody Groups

2016/07/07 by Matthew Westaway, Westaway, Matthew
Mathematics · #19C20 (Primary) 17B67 (Secondary) #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1607.02032

openalex publication_date 2016/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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