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 𝓓 defined by two derivations on this subalgebra. While 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 κ-deformation.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-11,
author = {Bruno Iochum and Thierry Masson and Andrzej Sitarz},
title = {$\kappa$-deformation, affine group and spectral triples},
journal = {Banach Center Publications},
volume = {97},
year = {2012},
pages = {261-291},
zbl = {1272.58014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-11}
}
Bruno Iochum; Thierry Masson; Andrzej Sitarz. κ-deformation, affine group and spectral triples. Banach Center Publications, Tome 97 (2012) pp. 261-291. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-11/