Labeled trees and localized automorphisms of the Cuntz algebras

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 O_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(O_n) 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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