On Conjugacy of Subalgebras of Graph C*-algebras

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

doi:10.1007/978-3-030-34072-8_17

On Conjugacy of Subalgebras of Graph C*-algebras

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

Institut for Matematik og Datalogi

Nagoya Institute of Technology

Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer review

Abstrakt

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.

Originalsprog	Engelsk
Titel	Geometric Methods in Physics XXXVII : Workshop 2018
Forlag	Birkhäuser Verlag
Publikationsdato	2019
Sider	163-173
ISBN (Trykt)	978-3-030-34071-1
ISBN (Elektronisk)	978-3-030-34072-8
DOI	https://doi.org/10.1007/978-3-030-34072-8_17
Status	Udgivet - 2019
Begivenhed	XXXIX Workshop on Geometric Methods in Physics - Varighed: 1. jul. 2018 → 7. jul. 2018

Konference

Konference	XXXIX Workshop on Geometric Methods in Physics
Periode	01/07/2018 → 07/07/2018

Navn	Trends in Mathematics

Dokumenter og links

10.1007/978-3-030-34072-8_17

1 Ph.d.-afhandling

Structure and symmetries in C*-algebras
Mikkelsen, S. E., 30. nov. 2021, Syddansk Universitet. Det Naturvidenskabelige Fakultet. 227 s.
Publikation: Afhandling › Ph.d.-afhandling

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Citationsformater

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title = "On Conjugacy of Subalgebras of Graph C*-algebras",

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.",

keywords = "C-functions, Cuntz algebra, MASA, S-functions, UHF-subalgebra, automorphism, graph C -algebra, inner and outer conjugacy",

author = "Mikkelsen, {Sophie Emma} and Wojciech Szymanski and Hong, {Jeong Hee} and Tomohiro Hayashi",

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T1 - On Conjugacy of Subalgebras of Graph C*-algebras

AU - Mikkelsen, Sophie Emma

AU - Szymanski, Wojciech

AU - Hong, Jeong Hee

AU - Hayashi, Tomohiro

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - C-functions

KW - Cuntz algebra

KW - MASA

KW - S-functions

KW - UHF-subalgebra

KW - automorphism

KW - graph C -algebra

KW - inner and outer conjugacy

U2 - 10.1007/978-3-030-34072-8_17

DO - 10.1007/978-3-030-34072-8_17

M3 - Article in proceedings

SN - 978-3-030-34071-1

T3 - Trends in Mathematics

SP - 163

EP - 173

BT - Geometric Methods in Physics XXXVII :

PB - Birkhäuser Verlag

T2 - XXXIX Workshop on Geometric Methods in Physics

Y2 - 1 July 2018 through 7 July 2018

ER -

On Conjugacy of Subalgebras of Graph C*-algebras

Abstrakt

Konference

Dokumenter og links

Fingeraftryk

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Structure and symmetries in C*-algebras

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