$\kappa$-deformation, affine group and spectral triples
Volume 98 / 2012
Banach Center Publications 98 (2012), 261-291
MSC: 58J42.
DOI: 10.4064/bc98-0-11
Abstract
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 $\mathcal D$ defined by two derivations on this subalgebra. While $\mathcal D$ has metric dimension two, the spectral dimension of the triple is one. This bypasses an obstruction described in [35] on existence of finitely-summable spectral triples for a compactified $\kappa$-deformation.
