Differential Calculi and Linear Connections
q-alg
2009-10-30 v1 dg-ga
Differential Geometry
Quantum Algebra
Abstract
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a one-to-one correspondence, between the module structure of the 1-forms and the metric torsion-free connections on it. In the commutative limit the connection remains as a shadow of the algebraic structure of the 1-forms.
Cite
@article{arxiv.q-alg/9601023,
title = {Differential Calculi and Linear Connections},
author = {Aristophanes Dimakis and J. Madore},
journal= {arXiv preprint arXiv:q-alg/9601023},
year = {2009}
}
Comments
16 pages of LaTeX