$\kappa$-deformation, affine group and spectral triples

Understand

A regular spectral triple is proposed for a two-dimensional $\kappa$-deformation.

• It is based on the naturally associated affine group $G$, a smooth subalgebra of $C^*(G)$, and an operator $\caD$ defined by two derivations on this subalgebra.
• While $\caD$ has metric dimension two, the spectral dimension of the triple is one.
• This bypasses an obstruction described in \cite{IochMassSchu11a} on existence of finitely-summable spectral triples for a compactified $\kappa$-deformation.