Spin group and almost commutative geometry

Abstract

For Connes' spectral triples, the group of automorphisms lifted to the Hilbert space is defined and used to fluctuate the metric. A few commutative examples are presented including Chamseddine and Connes' spectral unification of gravity and electromagnetism. One almost commutative example is treated: the full standard model. Here the lifted automorphisms explain O'Raifeartaigh's reduction $SU(2)\times U(3)/\zz_2.$

25 pages LaTeX, 1 figure, this paper will not be submitted to any journal, in particular not to Nucl.Phys.B

References in corpus (3)

• Hopf algebras, cyclic cohomology and the transverse index theory
• Anomaly Cancellation and gauge group of the standard model in NCG
• Standard model and unimodularity condition

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