Diagonal-preserving Isomorphisms of Algebras from Infinite Graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917072982769664 |
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| author | Eilers, Søren Ruiz, Efren |
| author_facet | Eilers, Søren Ruiz, Efren |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07917 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diagonal-preserving Isomorphisms of Algebras from Infinite Graphs Eilers, Søren Ruiz, Efren Operator Algebras Group Theory Rings and Algebras 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. |
| title | Diagonal-preserving Isomorphisms of Algebras from Infinite Graphs |
| topic | Operator Algebras Group Theory Rings and Algebras |
| url | https://arxiv.org/abs/2511.07917 |