On a Classification of Irreducible Almost-Commutative Geometries IV

Abstract

In this paper we will classify the finite spectral triples with KO-dimension six, following the classification found in [1,2,3,4], with up to four summands in the matrix algebra. Again, heavy use is made of Kra jewski diagrams [5]. Furthermore we will show that any real finite spectral triple in KO-dimension 6 is automatically S 0 -real. This work has been inspired by the recent paper by Alain Connes [6] and John Barrett [7]. In the classification we find that the standard model of particle physics in its minimal version fits the axioms of noncommutative geometry in the case of KO-dimension six. By minimal version it is meant that at least one neutrino has to be massless and mass-terms mixing particles and antiparticles are prohibited

Revised version for publication in the Journal of Mathematical Physics

References in corpus (3)

• On a Classification of Irreducible Almost-Commutative Geometries IV
• Almost-Commutative Geometry, massive Neutrinos and the Orientability Axiom in KO-Dimension 6
• Krajewski diagrams and spin lifts

Cited by in corpus (7)

• On a Classification of Irreducible Almost-Commutative Geometries IV
• Almost-Commutative Geometries Beyond the Standard Model III: Vector Doublets
• Almost-Commutative Geometry, massive Neutrinos and the Orientability Axiom in KO-Dimension 6
• Noncommutative geometry, topology and the standard model vacuum
• The Inverse Seesaw Mechanism in Noncommutative Geometry
• Gauge unification in noncommutative geometry
• Krajewski diagrams and the Standard Model