Noncommutative geodesics and the KSGNS construction
Abstract
We study geodesics in noncommutative geometry by means of bimodule connections and completely positive maps using the Kasparov, Stinespring, Gel'fand, Naimark & 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 real time. 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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