論文

査読有り
2015年8月

Topological full groups of one-sided shifts of finite type

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
  • Hiroki Matui

705
開始ページ
35
終了ページ
84
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1515/crelle-2013-0041
出版者・発行元
WALTER DE GRUYTER GMBH

We explore the topological full group [G] of an essentially principal etale groupoid G on a Cantor set. When G is minimal, we show that [G] (and its certain normal subgroup) is a complete invariant for the isomorphism class of the etale groupoid G. Furthermore, when G is either almost finite or purely infinite, the commutator subgroup D([G]) is shown to be simple. The etale groupoid G arising from a one-sided irreducible shift of finite type is a typical example of a purely infinite minimal groupoid. For such G, [G] is thought of as a generalization of the Higman-Thompson group. We prove that [G] is of type F-infinity, and so in particular it is finitely presented. This gives us a new infinite family of finitely presented infinite simple groups. Also, the abelianization of [G] is calculated and described in terms of the homology groups of G.

Web of Science ® 被引用回数 : 35

リンク情報
DOI
https://doi.org/10.1515/crelle-2013-0041
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000359196100003&DestApp=WOS_CPL

エクスポート
BibTeX RIS