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 |
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Keywords
- Cuntz algebra
- endomorphism
- automorphism
- permutation
- tree
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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 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 -