Linear Connections on Graphs

Details Linear Connections on Graphs Linear Connections on Graphs

1996-07-04

arxiv.org/abs/q-alg/9607004v2

Mathematics

Quantum Algebra

22pages, Latex file, Some errors corrected, To appear in J. Math. Phys

Scientific paper

10.1063/1.532172

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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