Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1899043 | Journal of Geometry and Physics | 2006 | 21 Pages |
Abstract
We introduce the notion of a pseudo-Riemannian spectral triple which generalizes the notion of spectral triple and allows for a treatment of pseudo-Riemannian manifolds within a noncommutative setting. It turns out that the relevant spaces in noncommutative pseudo-Riemannian geometry are not Hilbert spaces any more but Krein spaces, and Dirac operators are Krein-selfadjoint. We show that the noncommutative tori can be endowed with a pseudo-Riemannian structure in this way. For the noncommutative tori as well as for pseudo-Riemannian spin manifolds the dimension, the signature of the metric, and the integral of a function can be recovered from the spectral data.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Alexander Strohmaier,