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Noncommutative geodesics and the KSGNS construction
Journal of Geometry and Physics, Volume: 158, Start page: 103851
Swansea University Author:
Edwin Beggs
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DOI (Published version): 10.1016/j.geomphys.2020.103851
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...
| Published in: | Journal of Geometry and Physics |
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| ISSN: | 0393-0440 |
| Published: |
Elsevier BV
2020
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| Online Access: |
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| 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. |
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| Keywords: |
Noncommutative geometry; Differential geometry; Geodesic; Positive map; Hilbert C*module |
| College: |
Faculty of Science and Engineering |
| Start Page: |
103851 |