$\kappa$-Deformation and Spectral Triples

Bruno Iochum (1, 2, 3) , Thierry Masson (1, 2, 3) , Thomas Schucker (3, 1, 2) , Andrzej Sitarz (4)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332
3 CPT - E2 Géométrie, Physique et Symétries
4 Institute of Physics

The aim of the paper is to answer the following question: does $\kappa$-defor\-mation fit into the framework of noncommutative geometry in the sense of spectral triples? Using a compactification of time, we get a discrete version of $\kappa$-Minkowski deformation via $C^*$-algebras of groups. The dynamical system of the underlying groups (including some Baumslag--Solitar groups) is used in order to construct \emph{finitely summable} spectral triples. This allows to bypass an obstruction to finite-summability appearing when using the common regular representation.

Mots clés: Baumslag-Solitar groups; spectral triples; $\kappa$-deformation

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Bruno Iochum, Thierry Masson, Thomas Schucker, Andrzej Sitarz. $\kappa$-Deformation and Spectral Triples. Acta Physica Polonica B, 2011, 4 (3), pp.305. ⟨10.5506/APhysPolBSupp.4.305⟩. ⟨hal-00605453⟩