{"paper":{"title":"$K_2$ of Kac-Moody Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Matthew Westaway","submitted_at":"2016-07-07T14:23:26Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02032","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}