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arXiv · 1811.07601

Noncommutative geodesics and the KSGNS construction

Edwin J Beggs
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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 M_2(C) and C(Z_n), 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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Edwin J Beggs. 2018-11-19. Noncommutative geodesics and the KSGNS construction. https://arxiv.org/abs/1811.07601

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