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

B. Iochum; T. Masson; A. Sitarz

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

Mathematical Physics 2012-08-07 v1 High Energy Physics - Theory math.MP

Authors: B. Iochum , T. Masson , A. Sitarz

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 $\caD$ 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.

Keywords

noncommutative spacetime deformation quantization positive maps in quantum information

Cite

@article{arxiv.1208.1140,
  title  = {$\kappa$-deformation, affine group and spectral triples},
  author = {B. Iochum and T. Masson and A. Sitarz},
  journal= {arXiv preprint arXiv:1208.1140},
  year   = {2012}
}

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29 pages

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

Abstract

Keywords

Cite

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