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Projections, modules and connections for the noncommutative cylinder

Joakim Arnlind
•
Giovanni Landi
2020
  • journal article

Periodico
ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS
Abstract
We initiate a study of projections and modules over a noncommutative cylinder, a simple example of a noncompact noncommutative manifold. Since its algebraic structure turns out to have many similarities with the noncommutative torus, one can develop several concepts in a close analogy with the latter. In particular, we exhibit a countable number of nontrivial projections in the algebra of the noncommutative cylinder itself, and show that they provide concrete representatives for each class in the corresponding $K_0$ group. We also construct a class of bimodules endowed with connections of constant curvature. Furthermore, with the noncommutative cylinder considered from the perspective of pseudo-Riemannian calculi, we derive an explicit expression for the Levi-Civita connection and compute the Gaussian curvature.
DOI
10.4310/ATMP.2020.v24.n3.a1
WOS
WOS:000561364300001
Archivio
http://hdl.handle.net/11368/2970375
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85090423499
https://www.intlpress.com/site/pub/pages/journals/items/atmp/content/vols/0024/0003/a001/
Diritti
open access
FVG url
https://arts.units.it/request-item?handle=11368/2970375
Soggetti
  • Noncommutative geomet...

  • Noncommutative cylind...

  • Projection

  • Module

  • Connection

Scopus© citazioni
2
Data di acquisizione
Jun 7, 2022
Vedi dettagli
google-scholar
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