Full Cuntz–Krieger dilations via non-commutative boundaries

Adam Dor-On, Guy Salomon

Research output: Contribution to journalArticlepeer-review

Abstract

We apply Arveson's non-commutative boundary theory to dilate every TCK family of a directed graph G to a full CK family for G. We do this by describing all representations of the Toeplitz algebra T (G) that have a unique extension when restricted to the tensor algebra T+(G). This yields an alternative proof to a result of Katsoulis and Kribs that the C* -envelope of T+(G) is the CK algebra O(G). We then generalize our dilation results further, to the context of colored directed graphs, by investigating free products of operator algebras. These generalizations rely on results of independent interest on complete injectivity and a characterization of representations with the unique extension property for free products of operator algebras.

Original languageEnglish
Pages (from-to)416-438
Number of pages23
JournalJournal of the London Mathematical Society
Volume98
Issue number2
DOIs
StatePublished - Oct 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2018 London Mathematical Society

Keywords

  • 47A20
  • 47L55
  • 47L75
  • 47L80 (primary)

ASJC Scopus subject areas

  • General Mathematics

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