Modular vector fields in non-commutative geometry
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916793040240640 |
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| author | Taniguchi, Toyo |
| author_facet | Taniguchi, Toyo |
| contents | We construct a non-commutative analogue of the modular vector field on a Poisson manifold for a given pair of a double bracket and a connection on a space of 1-forms. The key ingredient, the triple divergence map, is directly constructed from a connection on a linear category to deal with multiple base points. As an application, we give an algebraic description of the framed, groupoid version of Turaev's loop operation $μ$ similar to the one obtained by Alekseev-Kawazumi-Kuno-Naef and the author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_24064 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modular vector fields in non-commutative geometry Taniguchi, Toyo Quantum Algebra Algebraic Topology Geometric Topology 57K20 (primary) 16D20, 16S34, 55P50, 58B34 (secondary) We construct a non-commutative analogue of the modular vector field on a Poisson manifold for a given pair of a double bracket and a connection on a space of 1-forms. The key ingredient, the triple divergence map, is directly constructed from a connection on a linear category to deal with multiple base points. As an application, we give an algebraic description of the framed, groupoid version of Turaev's loop operation $μ$ similar to the one obtained by Alekseev-Kawazumi-Kuno-Naef and the author. |
| title | Modular vector fields in non-commutative geometry |
| topic | Quantum Algebra Algebraic Topology Geometric Topology 57K20 (primary) 16D20, 16S34, 55P50, 58B34 (secondary) |
| url | https://arxiv.org/abs/2410.24064 |