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.
Projections, modules and connections for the noncommutative cylinder
Giovanni Landi
2020-01-01
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.File | Dimensione | Formato | |
---|---|---|---|
pdf.pdf
Accesso chiuso
Tipologia:
Documento in Versione Editoriale
Licenza:
Copyright Editore
Dimensione
6.8 MB
Formato
Adobe PDF
|
6.8 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
11368_2970375_print.pdf
accesso aperto
Tipologia:
Bozza finale post-referaggio (post-print)
Licenza:
Digital Rights Management non definito
Dimensione
7.41 MB
Formato
Adobe PDF
|
7.41 MB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.