Compact $\kappa$-deformation and spectral triples

Understand

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.