Endomorphisms of the Cuntz algebras and the Thompson groups

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Resumé

We investigate the relationship between endomorphisms of the Cuntz algebra O_2 and endomorphisms of the Thompson groups F, T and V represented inside the unitary group of O_2. For an endomorphism λ_u of O_2, we show that λ_u(V) is contained in V if and only if uεV. If λ_u is an automorphism of O_2 then uεV is equivalent to the containment of λ_u(F) in V. Our investigations are facilitated by introduction of the concept of modestly scaling endomorphism of O_n, whose properties and examples are investigated.
OriginalsprogEngelsk
TidsskriftStudia Mathematica
Antal sider11
ISSN0039-3223
StatusAccepteret/In press - 2017

Fingeraftryk

Thompson's Group
Cuntz Algebra
Endomorphism
Endomorphisms
Unitary group
Automorphism
Scaling
If and only if
Concepts
Relationships

Citer dette

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Endomorphisms of the Cuntz algebras and the Thompson groups. / Barlak, Selcuk; Hong, Jeong Hee; Szymanski, Wojciech.

I: Studia Mathematica, 2017.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Endomorphisms of the Cuntz algebras and the Thompson groups

AU - Barlak, Selcuk

AU - Hong, Jeong Hee

AU - Szymanski, Wojciech

PY - 2017

Y1 - 2017

N2 - We investigate the relationship between endomorphisms of the Cuntz algebra O_2 and endomorphisms of the Thompson groups F, T and V represented inside the unitary group of O_2. For an endomorphism λ_u of O_2, we show that λ_u(V) is contained in V if and only if uεV. If λ_u is an automorphism of O_2 then uεV is equivalent to the containment of λ_u(F) in V. Our investigations are facilitated by introduction of the concept of modestly scaling endomorphism of O_n, whose properties and examples are investigated.

AB - We investigate the relationship between endomorphisms of the Cuntz algebra O_2 and endomorphisms of the Thompson groups F, T and V represented inside the unitary group of O_2. For an endomorphism λ_u of O_2, we show that λ_u(V) is contained in V if and only if uεV. If λ_u is an automorphism of O_2 then uεV is equivalent to the containment of λ_u(F) in V. Our investigations are facilitated by introduction of the concept of modestly scaling endomorphism of O_n, whose properties and examples are investigated.

KW - Thompson's groups

KW - Cuntz algebra

KW - endomorphism

M3 - Journal article

JO - Studia Mathematica

JF - Studia Mathematica

SN - 0039-3223

ER -