Relation morphisms of directed graphs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915966371233792 |
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| author | de Castro, Gilles G. D'Andrea, Francesco Hajac, Piotr M. |
| author_facet | de Castro, Gilles G. D'Andrea, Francesco Hajac, Piotr M. |
| contents | Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphisms. As both functors are often used at the same time, finding a new category of graphs that allows a "common denominator" functor unifying the covariant and contravariant constructions is a fundamental problem. Herein, we solve this problem by first introducing the relation category of graphs RG, and then determining the concept of admissible graph relations that yields a subcategory of RG admitting a contravariant functor to k-Alg simultaneously generalizing the aforementioned covariant and contravariant functors. Although we focus on Leavitt path algebras and graph C*-algebras, on the way we unravel functors to k-Alg given by path algebras, Cohn path algebras and Toeplitz graph C*-algebras from suitable subcategories of RG. Better still, we illustrate relation morphisms of graphs by naturally occurring examples, including Cuntz algebras, quantum spheres and quantum balls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relation morphisms of directed graphs de Castro, Gilles G. D'Andrea, Francesco Hajac, Piotr M. Rings and Algebras Operator Algebras Quantum Algebra Primary: 16S88. Secondary: 46L85 Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphisms. As both functors are often used at the same time, finding a new category of graphs that allows a "common denominator" functor unifying the covariant and contravariant constructions is a fundamental problem. Herein, we solve this problem by first introducing the relation category of graphs RG, and then determining the concept of admissible graph relations that yields a subcategory of RG admitting a contravariant functor to k-Alg simultaneously generalizing the aforementioned covariant and contravariant functors. Although we focus on Leavitt path algebras and graph C*-algebras, on the way we unravel functors to k-Alg given by path algebras, Cohn path algebras and Toeplitz graph C*-algebras from suitable subcategories of RG. Better still, we illustrate relation morphisms of graphs by naturally occurring examples, including Cuntz algebras, quantum spheres and quantum balls. |
| title | Relation morphisms of directed graphs |
| topic | Rings and Algebras Operator Algebras Quantum Algebra Primary: 16S88. Secondary: 46L85 |
| url | https://arxiv.org/abs/2503.23343 |