Amenability of coarse spaces and K -algebras

Pere Ara, Kang Li, Fernando Lledó, Jianchao Wu

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

© 2017, The Author(s). In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally finite extended metric spaces and for general algebras over fields. In the context of algebras we also study the relation of amenability with proper infiniteness. We apply our general analysis to two important classes of algebras: the unital Leavitt path algebras and the translation algebras on locally finite extended metric spaces. In particular, we show that the amenability of a metric space is equivalent to the algebraic amenability of the corresponding translation algebra.
Original languageEnglish
Pages (from-to)257-306
JournalBulletin of Mathematical Sciences
Volume8
Issue number2
DOIs
Publication statusPublished - 1 Aug 2018

Keywords

  • Amenability
  • Coarse spaces
  • Følner nets
  • Leavitt path algebras
  • Paradoxical decompositions
  • Translation algebras
  • Unital K-algebras

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