$κ$-deformation, affine group and spectral triples

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

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