On a Classification of Irreducible Almost Commutative Geometries, A Second Helping

TL;DR

This paper completes the classification of irreducible almost commutative geometries relevant to particle physics by presenting four missing Krajewski diagrams after discussing spectral triples.

Contribution

It provides the final set of Krajewski diagrams completing the classification of these geometries, advancing the understanding of their structure in particle physics.

Findings

Four missing Krajewski diagrams identified and presented.

Complete classification of irreducible almost commutative geometries achieved.

Enhanced understanding of spectral triples in the context of particle physics.

Abstract

We complete the classification of almost commutative geometries from a particle physics point of view given in hep-th/0312276. Four missing Krajewski diagrams will be presented after a short introduction into irreducible, non-degenerate spectral triples.