2017/03/20 by Barlak, Selçuk, Hong, Jeong Hee, Szymanski, Wojciech
#FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1703.06798
We investigate the relationship between endomorphisms of the Cuntz algebra \mathcal O2 and endomorphisms of the Thompson groups F, T and V represented inside the unitary group of \mathcal O2. For an endomorphism λu of \mathcal O2, we show that λu(V)⊆ V if and only if u∈ V. If λu is an automorphism of \mathcal O2 then u∈ V is equivalent to λu(F)⊆ V. Our investigations are facilitated by introduction of the concept of modestly scaling endomorphism of \mathcal On, whose properties and examples are investigated.