Covariant connections on bicovariant differential calculus
| Autor: | Bhowmick, Jyotishman, Mukhopadhyay, Sugato |
|---|---|
| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2020.08.001 |
| Popis: | Given a bicovariant differential calculus $(\mathcal{E}, d)$ such that the braiding map is diagonalisable in a certain sense, the bimodule of two-tensors admits a direct sum decomposition into symmetric and anti-symmetric tensors. This is used to prove the existence of a bicovariant torsionless connection on $\mathcal{E}$. Following Heckenberger and Schm{\"u}dgen, we study invariant metrics and the compatibility of covariant connections with such metrics. A sufficient condition for the existence and uniqueness of bicovariant Levi-Civita connections is derived. This condition is shown to hold for cocycle deformations of classical Lie groups. Comment: Accepted for publication in Journal of Algebra |
| Databáze: | arXiv |
| Externí odkaz: |
|