Metrics and Pairs of Left and Right Connections on Bimodules
Abstract
Properties of metrics and pairs consisting of left and right connections are studied on the bimodules of differential 1-forms. Those bimodules are obtained from the derivation based calculus of an algebra of matrix valued functions, and an -covariant calculus of the quantum plane plane at a generic and the cubic root of unity. It is shown that, in the aforementioned examples, giving up the middle-linearity of metrics significantly enlarges the space of metrics. A~metric compatibility condition for the pairs of left and right connections is defined. Also, a compatibility condition between a left and right connection is discussed. Consequences entailed by reducing to the centre of a bimodule the domain of those conditions are investigated in detail. Alternative ways of relating left and right connections are considered.
Cite
@article{arxiv.q-alg/9602035,
title = {Metrics and Pairs of Left and Right Connections on Bimodules},
author = {L. Dcabrowski and P. M. Hajac and G. Landi and P. Siniscalco},
journal= {arXiv preprint arXiv:q-alg/9602035},
year = {2009}
}
Comments
16 pages, LaTeX, nofigures