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Noncommutative geodesics and the KSGNS construction

Edwin Beggs Orcid Logo

Journal of Geometry and Physics, Volume: 158, Start page: 103851

Swansea University Author: Edwin Beggs Orcid Logo

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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, Naĭmark & Segal (KSGNS) construction. This is motivated from classical geometry, and we also consider examples on the algebras M_2 and C(Z_n)thou...

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Published in: Journal of Geometry and Physics
ISSN: 0393-0440
Published: Elsevier BV 2020
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa54891
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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, Naĭmark & Segal (KSGNS) construction. This is motivated from classical geometry, and we also consider examples on the algebras M_2 and C(Z_n)though restricting to classical 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.
Keywords: Noncommutative geometry; Differential geometry; Geodesic; Positive map; Hilbert C*module
College: Faculty of Science and Engineering
Start Page: 103851