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More localized automorphisms of the Cuntz algebras

Part of: Selfadjoint operator algebras Topological dynamics

Published online by Cambridge University Press:  05 August 2010

Roberto Conti ,
Jason Kimberley  and
Wojciech Szymański
Roberto Conti
Affiliation:
Mathematics Department, School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia (roberto.conti@newcastle.edu.au; jason.kimberley@newcastle.edu.au)
Jason Kimberley
Affiliation:
Mathematics Department, School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia (roberto.conti@newcastle.edu.au; jason.kimberley@newcastle.edu.au)
Wojciech Szymański
Affiliation:
Mathematics Department, School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia (roberto.conti@newcastle.edu.au; jason.kimberley@newcastle.edu.au) Department of Mathematics and Computer Science, The University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark (szymanski@imada.sdu.dk)
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Abstract

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We completely determine the localized automorphisms of the Cuntz algebras corresponding to permutation matrices in Mn ⊗ Mn for n = 3 and n = 4. This result is obtained through a combination of general combinatorial techniques and large scale computer calculations. Our analysis proceeds according to the general scheme proposed in a previous paper, where we analysed in detail the case of using labelled rooted trees. We also discuss those proper endomorphisms of these Cuntz algebras which restrict to automorphisms of their respective diagonals. In the case of we compute the number of automorphisms of the diagonal induced by permutation matrices in M3 ⊗ M3 ⊗ M3.

Keywords

Cuntz algebraendomorphismautomorphismpermutationtree

MSC classification

Secondary: 46L40: Automorphisms 46L05: General theory of $C^*$-algebras 37B10: Symbolic dynamics
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 3 , October 2010 , pp. 619 - 631
Copyright
Copyright © Edinburgh Mathematical Society 2010

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Supplementary material: PDF

Conti Appendix

Conti Appendix

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