# Covariant connections on bicovariant differential calculus

@article{Bhowmick2019CovariantCO,
title={Covariant connections on bicovariant differential calculus},
journal={arXiv: Quantum Algebra},
year={2019}
}
• Published 10 December 2019
• Mathematics
• arXiv: Quantum Algebra
3 Citations
We prove that the $4D_\pm$ calculi on the quantum group $SU_q(2)$ satisfy a metric-independent sufficient condition for the existence of a unique bicovariant Levi-Civita connection corresponding to
• Mathematics
• 2022
Arbitrary right connections on bicovariant bimodules of a quantum group (Hopf algebra) are shown to canonically extend to tensor products of bicovariant bimodules. In particular, a connection on a
• Mathematics
• 2019
We study pseudo-Riemannian invariant metrics on bicovariant bimodules over Hopf algebras. We clarify some properties of such metrics and prove that pseudo-Riemannian invariant metrics on a

## References

SHOWING 1-10 OF 37 REFERENCES

• Mathematics
• 2016
We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a deformation of the

### Schmüdgen : Levi-Civita Connections on the Quantum Groups SLq(N) Oq(N) and Sp q (N)

• Comm. Math. Phys. 185,
• 1997
• Mathematics
• 2019
We study pseudo-Riemannian invariant metrics on bicovariant bimodules over Hopf algebras. We clarify some properties of such metrics and prove that pseudo-Riemannian invariant metrics on a
The paper deals with non-commutative differential geometry. The general theory of differential calculus on quantum groups is developed. Bicovariant bimodules as objects analogous to tensor bundles
Noncommutative Spaces It was noticed a long time ago that various properties of sets of points can be restated in terms of properties of certain commutative rings of functions over those sets. In
• Mathematics
• 2016
We prove the existence and uniqueness of Levi-Civita connections for a noncommutative pseudo-Riemannian metric on a class of centered bimodule of one forms. As an application, we compute the Ricci
• Mathematics
Reviews in Mathematical Physics
• 2020
We prove a Koszul formula for the Levi-Civita connection for any pseudo-Riemannian bilinear metric on a class of centered bimodule of noncommutative one-forms. As an application to the Koszul