# Temporal Lorentzian Spectral Triples

September 02, 2014

We present the notion of temporal Lorentzian spectral triple which is an
extension of the notion of pseudo-Riemannian spectral triple with a way to
ensure that the signature of the metric is Lorentzian. A temporal Lorentzian
spectral triple corresponds to a specific 3+1 decomposition of a possibly
noncommutative Lorentzian space. This structure introduces a notion of global
time in noncommutative geometry. As an example, we construct a noncommutative
Minkowsky spacetime with the use of a degenerate Moyal product.

Keywords:

noncommutative geometry, Lorentzian geometry, spectral triples