Linear Connections on Graphs
q-alg
2016-09-08 v2 量子代数
摘要
In recent years, discrete spaces such as graphs attract much attention as models for physical spacetime or as models for testing the spirit of non-commutative geometry. In this work, we construct the differential algebras for graphs by extending the work of Dimakis et al and discuss linear connections and curvatures on graphs. Especially, we calculate connections and curvatures explicitly for the general nonzero torsion case. There is a metric, but no metric-compatible connection in general except the complete symmetric graph with two vertices.
引用
@article{arxiv.q-alg/9607004,
title = {Linear Connections on Graphs},
author = {Sunggoo Cho and Kwang Sung Park},
journal= {arXiv preprint arXiv:q-alg/9607004},
year = {2016}
}
备注
22pages, Latex file, Some errors corrected, To appear in J. Math. Phys