Foundations of Noncommutative Carrollian Geometry via Lie-Rinehart Pairs
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911484161818624 |
|---|---|
| author | Bruce, Andrew James |
| author_facet | Bruce, Andrew James |
| contents | Carrollian manifolds offer an intrinsic geometric framework for the physics in the ultra-relativistic limit. The recently introduced Carrollian Lie algebroids are generalised to the setting of $ρ$-commutative geometry, (also known as almost commutative geometry), where the underlying algebras commute up to a numerical factor. Via $ρ$-Lie-Rinehart pairs, it is shown that the foundational tenets of Carrollian geometry have analogous statements in the almost commutative world. We explicitly build two toy examples: we equip the extended quantum plane and the noncommutative $2$-torus with Carrollian structures. This opens up the rigorous study of noncommutative Carrollian geometry via almost commutative geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19458 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Foundations of Noncommutative Carrollian Geometry via Lie-Rinehart Pairs Bruce, Andrew James Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry Quantum Algebra 14A22, 16W50, 17B70, 83C65 Carrollian manifolds offer an intrinsic geometric framework for the physics in the ultra-relativistic limit. The recently introduced Carrollian Lie algebroids are generalised to the setting of $ρ$-commutative geometry, (also known as almost commutative geometry), where the underlying algebras commute up to a numerical factor. Via $ρ$-Lie-Rinehart pairs, it is shown that the foundational tenets of Carrollian geometry have analogous statements in the almost commutative world. We explicitly build two toy examples: we equip the extended quantum plane and the noncommutative $2$-torus with Carrollian structures. This opens up the rigorous study of noncommutative Carrollian geometry via almost commutative geometry. |
| title | Foundations of Noncommutative Carrollian Geometry via Lie-Rinehart Pairs |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry Quantum Algebra 14A22, 16W50, 17B70, 83C65 |
| url | https://arxiv.org/abs/2510.19458 |