2023/09/02 by Nawata, Norio
#46L40 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L55 #Secondary 46L35
paper · doi:10.48550/arxiv.2309.00934
Let \mathfrakC be the smallest class of countable discrete groups with the following properties: (i) \mathfrakC contains the trivial group, (ii) \mathfrakC is closed under isomorphisms, countable increasing unions and extensions by ℤ. Note that \mathfrakC contains all countable discrete torsion-free abelian groups and poly-ℤ groups. Also, \mathfrakC is a subclass of the class of countable discrete torsion-free elementary amenable groups. In this paper, we show that if Γ∈ \mathfrakC, then all strongly outer actions of Γ on the Razak-Jacelon algebra W are cocycle conjugate to each other. This can be regarded as an analogous result of Szabó's result for strongly self-absorbing C^*-algebras.