On two notions of torsion and metric compatibility of connections in noncommutative geometry
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909788680486912 |
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| author | Bhowmick, Jyotishman Ghosh, Bappa Guin, Satyajit |
| author_facet | Bhowmick, Jyotishman Ghosh, Bappa Guin, Satyajit |
| contents | We compare the notions of metric-compatibility and torsion of a connection in the frameworks of Beggs-Majid and Mesland-Rennie. It follows that for $\ast$-preserving connections, compatibility with a real metric in the sense of Beggs-Majid corresponds to Hermitian connections in the sense of Mesland-Rennie. If the calculus is quasi-tame, the torsion zero conditions are equivalent. A combination of these results proves the existence and uniqueness of Levi-Civita connections in the sense of Mesland-Rennie for unitary cocycle deformations of a large class of Riemannian manifolds as well as the Heckenberger-Kolb calculi on all quantized irreducible flag manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11888 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On two notions of torsion and metric compatibility of connections in noncommutative geometry Bhowmick, Jyotishman Ghosh, Bappa Guin, Satyajit Quantum Algebra Mathematical Physics Operator Algebras We compare the notions of metric-compatibility and torsion of a connection in the frameworks of Beggs-Majid and Mesland-Rennie. It follows that for $\ast$-preserving connections, compatibility with a real metric in the sense of Beggs-Majid corresponds to Hermitian connections in the sense of Mesland-Rennie. If the calculus is quasi-tame, the torsion zero conditions are equivalent. A combination of these results proves the existence and uniqueness of Levi-Civita connections in the sense of Mesland-Rennie for unitary cocycle deformations of a large class of Riemannian manifolds as well as the Heckenberger-Kolb calculi on all quantized irreducible flag manifolds. |
| title | On two notions of torsion and metric compatibility of connections in noncommutative geometry |
| topic | Quantum Algebra Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2509.11888 |