Covariant connections on bicovariant differential calculus
Journal of Algebra
Given a bicovariant differential calculus (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 E. Following Heckenberger and Schmüdgen, 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.
Bhowmick, Jyotishman and Mukhopadhyay, Sugato, "Covariant connections on bicovariant differential calculus" (2020). Journal Articles. 46.