Compact $κ$-deformation and spectral triples

Details Compact $κ$-deformation and spectral triples Compact $κ$-deformation and spectral triples

2010-04-23

arxiv.org/abs/1004.4190v2

Physics

High Energy Physics

High Energy Physics - Theory

30 pages

Scientific paper

10.1016/S0034-4877(11)60026-8

We construct discrete versions of $\kappa$-Minkowski space related to a certain compactness of the time coordinate. We show that these models fit into the framework of noncommutative geometry in the sense of spectral triples. The dynamical system of the underlying discrete groups (which include some Baumslag--Solitar groups) is heavily used in order to construct \emph{finitely summable} spectral triples. This allows to bypass an obstruction to finite-summability appearing when using the common regular representation. The dimension of these spectral triples is unrelated to the number of coordinates defining the $\kappa$-deformed Minkowski spaces.

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