On Conjugacy of Subalgebras of Graph C*-algebras

Sophie Emma Mikkelsen, Wojciech Szymanski, Jeong Hee Hong, Tomohiro Hayashi

Publikation: Kapitel i bog/rapport/konference-proceedingKonferencebidrag i proceedingsForskningpeer review


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 a is a vertex-fixing quasi-free automorphism
of the corresponding graph C*-algebra C*(E) such that a(D_E)\neq D_E,
where D_E is the canonical MASA in C*(E), then a(D_E)\neq wDEw* for
all unitaries w in C*(E). That is, the two MASAs D_E and a(D_E) 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.
TitelGeometric Methods in Physics XXXVII : Workshop 2018
ForlagBirkhäuser Verlag
ISBN (Trykt)978-3-030-34071-1
ISBN (Elektronisk)978-3-030-34072-8
StatusUdgivet - 2019
BegivenhedXXXIX Workshop on Geometric Methods in Physics -
Varighed: 1. jul. 20187. jul. 2018


KonferenceXXXIX Workshop on Geometric Methods in Physics
NavnTrends in Mathematics


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