On endomorphisms of the Cuntz algebra which preserve the canonical UHF-subalgebra, II

Hayashi, T.; Hong, Jeong Hee; Szymański, Wojciech

doi:10.1016/j.jfa.2016.07.004

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2017

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“…However, it should be noted that there exist unitaries u ∈ U (O n ) which do not belong to F n for which nevertheless we have λ u (F n ) ⊆ F n . Such exotic endomorphisms of O n have been thoroughly investigated in [5], [10] and [11].…”

Section: The Main Resultsmentioning

confidence: 99%

Endomorphisms of the Cuntz Algebras and the Thompson Groups

Barlak,

Hong,

Szymanski

2017

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We investigate the relationship between endomorphisms of the Cuntz algebra O2 and endomorphisms of the Thompson groups F , T and V represented inside the unitary group of O2. For an endomorphism λu of O2, we show that λu(V ) ⊆ V if and only if u ∈ V . If λu is an automorphism of O2 then u ∈ V is equivalent to λu(F ) ⊆ V . Our investigations are facilitated by introduction of the concept of modestly scaling endomorphism of On, whose properties and examples are investigated.

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Section: The Main Resultsmentioning

confidence: 99%