κ-deformation, affine group and spectral triples

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2012Embargo end date: 01 Jan 2012 English Publisher:Institute of Mathematics, Polish Academy of SciencesJournal:Banach Center Publications, volume 98, pages 261-291 (issn: 0137-6934, eissn: 1730-6299,

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Authors: Iochum, Bruno; Masson, T.; Sitarz, A.;

doi: 10.4064/bc98-0-11 , 10.48550/arxiv.1208.1140

arXiv: 1208.1140

κ-deformation, affine group and spectral triples

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Abstract

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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High Energy Physics - Theory, High Energy Physics - Theory (hep-th), FOS: Physical sciences, [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], Mathematical Physics (math-ph), [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph], [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], Mathematical Physics

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