https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 More localized automorphisms of the Cuntz algebras https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:4295 Wed 11 Apr 2018 12:01:28 AEST ]]> Computing the Jones index of quadratic permutation endomorphisms of O₂ https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:7685 Sat 24 Mar 2018 08:33:34 AEDT ]]> Labeled trees and localized automorphisms of the Cuntz algebras https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:17881 n which preserve both the diagonal and the core UHFsubalgebra. A general criterion of invertibility of endomorphisms yielding such automorphisms is given. Combinatorial investigations of endomorphisms related to permutation matrices are presented. Key objects entering this analysis are labeled rooted trees equipped with additional data. Our analysis provides insight into the structure of Aut(On) and leads to numerous new examples. In particular, we completely classify all such automorphisms of O₂ for the permutation unitaries in ⊗⁴M₂. We show that the subgroup of Out(O₂) generated by these automorphisms contains a copy of the infinite dihedral group Z ⋊ Z₂.]]> Sat 24 Mar 2018 07:56:19 AEDT ]]>