Gluing topological graph C*-algebras
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909687763435520 |
|---|---|
| author | Gothe, Atul Quigg, John Tobolski, Mariusz |
| author_facet | Gothe, Atul Quigg, John Tobolski, Mariusz |
| contents | We introduce regular closed subgraphs of Katsura's topological graphs and use them to generalize the notion of an adjunction space from topology. Our construction attaches a topological graph onto another via a regular factor map. We prove that under suitable assumptions the C*-algebra of the adjunction graph is a pullback of the C*-algebras of the topological graphs being glued. Our results generalize certain pushout-to-pullback theorems proved in the context of discrete directed graphs. Our theorem applied to homeomorphism C*-algebras recovers a special case of the well-known result stating that pullbacks of $\mathbb{Z}$-C*-algebras induce pullbacks of the respective crossed product C*-algebras. Furthermore, we show that the C*-algebras of odd-dimensional quantum balls of Hong and Szymański (which are known not to be graph C*-algebras) are topological graph C*-algebras and we recover the pullback structure of C*-algebras of odd-dimensional quantum spheres by gluing the topological graphs associated to the C*-algebras of the corresponding odd-dimensional quantum balls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11592 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gluing topological graph C*-algebras Gothe, Atul Quigg, John Tobolski, Mariusz Operator Algebras 46L05, 46L55, 46L85 We introduce regular closed subgraphs of Katsura's topological graphs and use them to generalize the notion of an adjunction space from topology. Our construction attaches a topological graph onto another via a regular factor map. We prove that under suitable assumptions the C*-algebra of the adjunction graph is a pullback of the C*-algebras of the topological graphs being glued. Our results generalize certain pushout-to-pullback theorems proved in the context of discrete directed graphs. Our theorem applied to homeomorphism C*-algebras recovers a special case of the well-known result stating that pullbacks of $\mathbb{Z}$-C*-algebras induce pullbacks of the respective crossed product C*-algebras. Furthermore, we show that the C*-algebras of odd-dimensional quantum balls of Hong and Szymański (which are known not to be graph C*-algebras) are topological graph C*-algebras and we recover the pullback structure of C*-algebras of odd-dimensional quantum spheres by gluing the topological graphs associated to the C*-algebras of the corresponding odd-dimensional quantum balls. |
| title | Gluing topological graph C*-algebras |
| topic | Operator Algebras 46L05, 46L55, 46L85 |
| url | https://arxiv.org/abs/2506.11592 |