3 Citations
Levi-Civita connection for $SU_q(2)$
- Mathematics
- 2020
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…
Metric compatibility and Levi-Civita Connections on Quantum Groups
- 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…
Pseudo-Riemannian metrics on bicovariant bimodules
- 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
Noncommutative Principal Bundles Through Twist Deformation
- 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
Pseudo-Riemannian metrics on bicovariant bimodules
- 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…
Differential calculus on compact matrix pseudogroups (quantum groups)
- Mathematics
- 1989
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 Geometry
- Mathematics
- 1997
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…
A new look at Levi-Civita connection in noncommutative geometry
- 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…
On the Koszul formula in noncommutative geometry
- MathematicsReviews 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…