Equivariant Lorentzian Spectral Triples

TL;DR

This paper introduces equivariant noncommutative Lorentzian spectral geometries, constructing spectral triples compatible with indefinite metrics and computing the spectrum of the Dirac operator.

Contribution

It provides explicit examples of equivariant Lorentzian spectral triples, extending noncommutative geometry to indefinite metric settings.

Findings

Constructed examples of equivariant Lorentzian spectral triples.

Calculated the spectrum of the equivariant Dirac operator.

Extended spectral triple framework to Lorentzian (indefinite) metrics.

Abstract

We present examples of equivariant noncommutative Lorentzian spectral geometries. The equivariance with respect to a compact isometry group (or quantum group) allows to construct the algebraic data of a version of spectral triple geometry adapted to the situation of an indefinite metric. The spectrum of the equivariant Dirac operator is calculated.