Pseudo-Riemannian Metrics in Models Based on Noncommutative Geometry
General Relativity and Quantum Cosmology
2011-04-15 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
Several examples and models based on noncommutative differential calculi on commutative algebras indicate that a metric should be regarded as an element of the left-linear tensor product of the space of 1-forms with itself. We show how the metric compatibility condition with a linear connection generalizes to this framework.
Cite
@article{arxiv.gr-qc/9908022,
title = {Pseudo-Riemannian Metrics in Models Based on Noncommutative Geometry},
author = {Aristophanes Dimakis and Folkert Muller-Hoissen},
journal= {arXiv preprint arXiv:gr-qc/9908022},
year = {2011}
}
Comments
7 pages, contribution to 8th Colloquium on Quantum Groups and Integrable Systems, Prague, June 1999