Groupoids and C-algebras for categories of paths

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16 Scopus citations

Abstract

In this paper we describe a new method of defining C-algebras from oriented combinatorial data, thereby generalizing the construction of algebras from directed graphs, higher-rank graphs, and ordered groups. We show that only the most elementary notions of concatenation and cancellation of paths are required to define versions of Cuntz-Krieger and Toeplitz-Cuntz- Krieger algebras, and the presentation by generators and relations follows naturally. We give sufficient conditions for the existence of an AF core, hence of the nuclearity of the C-algebras, and for aperiodicity, which is used to prove the standard uniqueness theorems.

Original languageEnglish (US)
Pages (from-to)5771-5819
Number of pages49
JournalTransactions of the American Mathematical Society
Volume366
Issue number11
DOIs
StatePublished - Jan 1 2014

Keywords

  • Aperiodicity
  • Cuntz-Krieger algebra
  • Groupoid
  • Toeplitz Cuntz-Krieger algebra

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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