Dixmier traces on noncompact isospectral deformations |
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Authors: | Victor Gayral Joseph C Várilly |
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Institution: | a Matematisk Afdeling, Universitetsparken 5, 2100 København, Denmark b Centre de Physique Théorique33Unité Mixte de Recherche 6207., CNRS-Luminy, Case 907, 13288 Marseille Cedex 9, France c Departamento de Matemáticas, Universidad de Costa Rica, 2060 San José, Costa Rica |
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Abstract: | We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group Rl. Under deformation by a torus action, a standard formula relates Dixmier traces of measurable operators to integrals of functions on the manifold. We show that this relation persists for actions of Rl, under mild restrictions on the geometry of the manifold which guarantee the Dixmier traceability of those operators. |
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Keywords: | Dixmier trace Dirac operator Moyal product Isospectral deformation |
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