dorsal/arxiv
View SchemaLinear Connections on Graphs
| Authors | Sunggoo Cho, Kwang Sung Park |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9607004 |
| URL | https://arxiv.org/abs/q-alg/9607004 |
| DOI | 10.1063/1.532172 |
Abstract
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.
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"abstract": "In recent years, discrete spaces such as graphs attract much attention as\nmodels for physical spacetime or as models for testing the spirit of\nnon-commutative geometry. In this work, we construct the differential algebras\nfor graphs by extending the work of Dimakis et al and discuss linear\nconnections and curvatures on graphs. Especially, we calculate connections and\ncurvatures explicitly for the general nonzero torsion case. There is a metric,\nbut no metric-compatible connection in general except the complete symmetric\ngraph with two vertices.",
"arxiv_id": "q-alg/9607004",
"authors": [
"Sunggoo Cho",
"Kwang Sung Park"
],
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"doi": "10.1063/1.532172",
"title": "Linear Connections on Graphs",
"url": "https://arxiv.org/abs/q-alg/9607004"
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