- Title
- Labeled trees and localized automorphisms of the Cuntz algebras
- Creator
- Conti, Roberto; Szymanski, Wojciech
- Relation
- Transactions of the American Mathematical Society Vol. 363, Issue 11, p. 5847-5870
- Publisher Link
- http://dx.doi.org/10.1090/s0002-9947-2011-05234-7
- Publisher
- American Mathematical Society
- Resource Type
- journal article
- Date
- 2011
- Description
- We initiate a detailed and systematic study of automorphisms of the Cuntz algebras On 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.
- Subject
- Cuntz algebra; endomorphism; automorphism; Cartan subalgebra; core UHF-subalgebra; normalizer; permutation; tree
- Identifier
- http://hdl.handle.net/1959.13/1065644
- Identifier
- uon:17881
- Identifier
- ISSN:0002-9947
- Language
- eng
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