Abstract
We study geodesics in noncommutative geometry by means of bimodule connections and completely positive maps using the Kasparov, Stinespring, Gel’fand, Naĭmark & Segal (KSGNS) construction. This is motivated from classical geometry, and we also consider examples on the algebras M2(ℂ) and C(Zn), though restricting to classical time t∈R. On the way we have to consider the reality of a noncommutative vector field, and for this we propose a definition depending on a state on the algebra.
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