More localized automorphisms of the Cuntz algebras
Roberto Conti, Jason Kimberley, Wojciech Szymanski

TL;DR
This paper classifies localized automorphisms of Cuntz algebras $O_n$ for $n=3,4$ using combinatorial and computational methods, extending previous analyses for $O_2$ and exploring diagonal automorphisms.
Contribution
It provides a complete classification of certain localized automorphisms of $O_3$ and $O_4$, employing novel combinatorial and computational techniques.
Findings
Classified localized automorphisms for $O_3$ and $O_4$
Determined automorphisms of diagonals induced by permutation matrices
Extended analysis framework from $O_2$ to higher $n$
Abstract
We completely determine the localized automorphisms of the Cuntz algebras corresponding to permutation matrices in for and . 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 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 we compute the number of automorphisms of the diagonal induced by permutation matrices in .
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