Projections, modules and connections for the noncommutative cylinder
| Autor: | Giovanni Landi, Joakim Arnlind |
|---|---|
| Přispěvatelé: | Arnlind, Joakim, Landi, Giovanni |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Noncommutative geometry Noncommutative cylinder Projections Modules Connections Algebraic structure General Mathematics General Physics and Astronomy FOS: Physical sciences Module Simple (abstract algebra) Mathematics::K-Theory and Homology Mathematics::Quantum Algebra Connection Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) Projection Noncommutative torus Mathematical Physics Mathematics Group (mathematics) Mathematics::Operator Algebras Mathematical Physics (math-ph) Manifold Connection (mathematics) Constant curvature Mathematics::Differential Geometry |
| Popis: | 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. v3: Proposition 4.5 improved; One corollary removed; Scientific content unchanged |
| Databáze: | OpenAIRE |
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