Quantum Riemannian geometry of quantum projective spaces
Quantum Algebra
2022-07-15 v2 Mathematical Physics
math.MP
Abstract
We study the quantum Riemannian geometry of quantum projective spaces of any dimension. In particular we compute the Riemann and Ricci tensors, using previously introduced quantum metrics and quantum Levi-Civita connections. We show that the Riemann tensor is a bimodule map and derive various consequences of this fact. We prove that the Ricci tensor is proportional to the quantum metric, giving a quantum analogue of the Einstein condition, and compute the corresponding scalar curvature. Along the way we also prove several results for various objects related to those mentioned here.
Cite
@article{arxiv.2103.06083,
title = {Quantum Riemannian geometry of quantum projective spaces},
author = {Marco Matassa},
journal= {arXiv preprint arXiv:2103.06083},
year = {2022}
}
Comments
33 pages, v2: minor corrections, accepted for publication