Fubini-Study metrics and Levi-Civita connections on quantum projective spaces
| Autor: | Matassa, Marco |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Advances in Mathematics, 393 (2021): 108101 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.aim.2021.108101 |
| Popis: | We introduce analogues of the Fubini-Study metrics and the corresponding Levi-Civita connections on quantum projective spaces. We define the quantum metrics as two-tensors, symmetric in the appropriate sense, in terms of the differential calculi introduced by Heckenberger and Kolb. We define connections on these calculi and show that they are torsion free and cotorsion free, where the latter condition uses the quantum metric and is a weaker notion of metric compatibility. Finally we show that these connections are bimodule connections and that the metric compatibility also holds in a stronger sense. Comment: 42 pages. v4: minor corrections to the published version. Fixed an erroneous sign in equation (4.2); generalized the statement of Lemma 5.4 (which was only valid in the quadratic case) |
| Databáze: | arXiv |
| Externí odkaz: |
|