Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.16304 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909582010351616 |
|---|---|
| author | Liu, Zuan Malbos, Philippe |
| author_facet | Liu, Zuan Malbos, Philippe |
| contents | This paper introduces the structure of operated polygraphs as a categorical model for rewriting in operated algebras, generalizing Gröbner-Shirshov bases with non-monomial termination orders. We provide a combinatorial description of critical branchings of operated polygraphs using the structure of polyautomata that we introduce in this paper. Polyautomata extend linear polygraphs equipped with an operator structure formalized by a pushdown automaton. We show how to construct polygraphic resolutions of free operated algebras from their confluent and terminating presentations. Finally, we apply our constructions to several families of operated algebras, including Rota-Baxter algebras, differential algebras, and differential Rota-Baxter algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polygraphic resolutions for operated algebras Liu, Zuan Malbos, Philippe Rings and Algebras Formal Languages and Automata Theory Category Theory 12H05, 16Z10, 18N30, 68Q42, 18G10 This paper introduces the structure of operated polygraphs as a categorical model for rewriting in operated algebras, generalizing Gröbner-Shirshov bases with non-monomial termination orders. We provide a combinatorial description of critical branchings of operated polygraphs using the structure of polyautomata that we introduce in this paper. Polyautomata extend linear polygraphs equipped with an operator structure formalized by a pushdown automaton. We show how to construct polygraphic resolutions of free operated algebras from their confluent and terminating presentations. Finally, we apply our constructions to several families of operated algebras, including Rota-Baxter algebras, differential algebras, and differential Rota-Baxter algebras. |
| title | Polygraphic resolutions for operated algebras |
| topic | Rings and Algebras Formal Languages and Automata Theory Category Theory 12H05, 16Z10, 18N30, 68Q42, 18G10 |
| url | https://arxiv.org/abs/2502.16304 |