Noncommutative geodesics and the KSGNS construction

[摘要] 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 time t is an element of 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. (C) 2020 Elsevier B.V. All rights reserved.

[发布日期] 2020-12-01

[关键词] Noncommutative geometry;Differential geometry;Geodesic;Positive map;Hilbert C* module