### Abstract

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 language | English |
---|---|

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 53 |

Issue number | 3 |

Pages (from-to) | 619-631 |

Number of pages | 12 |

ISSN | 0013-0915 |

DOIs | |

Publication status | Published - 1. Oct 2010 |

### Fingerprint

### Keywords

- Cuntz algebra
- endomorphism
- automorphism
- permutation
- tree

### Cite this

*Proceedings of the Edinburgh Mathematical Society*,

*53*(3), 619-631. https://doi.org/10.1017/S0013091508000886

}

*Proceedings of the Edinburgh Mathematical Society*, vol. 53, no. 3, pp. 619-631. https://doi.org/10.1017/S0013091508000886

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

Research output: Contribution to journal › Conference article › Research › peer-review

TY - GEN

T1 - More localized automorphisms of the Cuntz algebras

AU - Conti, Roberto

AU - Kimberley, Jason

AU - Szymanski, Wojciech

PY - 2010/10/1

Y1 - 2010/10/1

N2 - 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.

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.

KW - Cuntz algebra

KW - endomorphism

KW - automorphism

KW - permutation

KW - tree

U2 - 10.1017/S0013091508000886

DO - 10.1017/S0013091508000886

M3 - Conference article

VL - 53

SP - 619

EP - 631

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 3

ER -