# On a classification of irreducible almost-commutative geometries. IV

#### Autoren: Jan-Hendrik Jureit, Christoph Stephan (2008)

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 Krajewski 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

Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
Seiten:
33502
Band:
49, no. 3

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