On Conjugacy of Subalgebras of Graph C*-algebras

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Abstract

The problem of inner vs outer conjugacy of subalgebras of certain graph C*-algebras is investigated. For a large class of finite graphs E, we show that whenever α is a vertex-fixing quasi-free automorphism of the corresponding graph C*-algebra C* (E) such that α(DE) ≠ DE where DE is the canonical MASA in C*(E), then α(DE) ≠ ωDEω* for all unitaries ω ∈ C* (E). That is, the two MASAs DE and α(DE) of C*(E) are outer but not inner conjugate. For the Cuntz algebras On, we find a criterion which guarantees that a polynomial automorphism moves the canonical UHF subalgebra to a non-inner conjugate UHF subalgebra. The criterion is phrased in terms of rescaling of trace on diagonal projections.
Original languageEnglish
Title of host publicationGeometric Methods in Physics XXXVII : Workshop 2018
PublisherBirkhäuser Verlag
Publication date2019
Pages163-173
ISBN (Print)978-3-030-34071-1
ISBN (Electronic)978-3-030-34072-8
DOIs
Publication statusPublished - 2019
EventXXXIX Workshop on Geometric Methods in Physics -
Duration: 1. Jul 20187. Jul 2018

Conference

ConferenceXXXIX Workshop on Geometric Methods in Physics
Period01/07/201807/07/2018
SeriesTrends in Mathematics

Keywords

  • C-functions
  • Cuntz algebra
  • MASA
  • S-functions
  • UHF-subalgebra
  • automorphism
  • graph C -algebra
  • inner and outer conjugacy

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