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arXiv · 2511.07917

Diagonal-preserving Isomorphisms of Algebras from Infinite Graphs

Søren Eilers·Efren Ruiz
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Abstract

We establish logical equivalence between statements involving * the Cuntz C*-algebra $\mathcal O_\infty$ with its canonical diagonal; * graph C*-algebras with their canonical diagonals; * Leavitt path algebras over general fields with their canonical diagonals; * Leavitt path algebras over $\mathbb Z$; * topological full groups; * groupoids; and * the automorphism $x\mapsto -x$ on certain $K_0$- and homology groups equal to $\mathbb Z$ Deciding whether these equivalent statements are true or false is of importance in studies of geometric classification of diagonal-preserving isomorphism between graph C*-algebras and Leavitt path algebras, mirroring a similar hindrance studied by Cuntz more than 40 years ago.

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Søren Eilers, Efren Ruiz. 2025-11-11. Diagonal-preserving Isomorphisms of Algebras from Infinite Graphs. https://arxiv.org/abs/2511.07917

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