More localized automorphisms of the Cuntz algebras

Roberto Conti, Jason Kimberley, Wojciech Szymanski

Research output: Contribution to journalConference articleResearchpeer-review

Abstract

We completely determine the localized automorphisms of the Cuntz algebras O_n corresponding to permutation matrices in M_n \otimes M_n 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 analyzed in detail the case of O_2 using labeled rooted trees. We also discuss those proper endomorphisms of these Cuntz algebras which restrict to automorphisms of their respective diagonals.
In the case of O_3 we compute the number of automorphisms of the diagonal induced by permutation matrices in M_3 \otimes M_3 \otimes M_3.
Original languageEnglish
JournalProceedings of the Edinburgh Mathematical Society
Volume53
Issue number3
Pages (from-to)619-631
Number of pages12
ISSN0013-0915
DOIs
Publication statusPublished - 1. Oct 2010

Fingerprint

Cuntz Algebra
Automorphisms
Permutation Matrix
Labeled Trees
Rooted Trees
Endomorphisms

Keywords

  • Cuntz algebra
  • endomorphism
  • automorphism
  • permutation
  • tree

Cite this

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title = "More localized automorphisms of the Cuntz algebras",
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More localized automorphisms of the Cuntz algebras. / Conti, Roberto; Kimberley, Jason; Szymanski, Wojciech.

In: Proceedings of the Edinburgh Mathematical Society, Vol. 53, No. 3, 01.10.2010, p. 619-631.

Research output: Contribution to journalConference articleResearchpeer-review

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AB - We completely determine the localized automorphisms of the Cuntz algebras O_n corresponding to permutation matrices in M_n \otimes M_n 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 analyzed in detail the case of O_2 using labeled rooted trees. We also discuss those proper endomorphisms of these Cuntz algebras which restrict to automorphisms of their respective diagonals. In the case of O_3 we compute the number of automorphisms of the diagonal induced by permutation matrices in M_3 \otimes M_3 \otimes M_3.

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