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κ-deformation, affine group and spectral triples

Bruno IochumThierry MassonAndrzej Sitarz — 2012

Banach Center Publications

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.

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