1304.7583 (Ali H. Chamseddine et al.)

Inner Fluctuations in Noncommutative Geometry without the first order
condition    [PDF]

Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom

We extend inner fluctuations to spectral triples that do not fulfill the first-order condition. This involves the addition of a quadratic term to the usual linear terms. We find a semi-group of inner fluctuations, which only depends on the involutive algebra A and which extends the unitary group of A. This has a key application in noncommutative spectral models beyond the Standard Model, of which we consider here a toy model.

View original: http://arxiv.org/abs/1304.7583