$\kappa$-Deformation and Spectral Triples

TL;DR

This paper investigates whether $$-deformation can be incorporated into noncommutative geometry through spectral triples, constructing finitely summable triples via group $C^*$-algebras and dynamical systems.

Contribution

It introduces a novel approach to $$-deformation using compactification and group $C^*$-algebras to achieve finitely summable spectral triples.

Findings

Constructed finitely summable spectral triples for $$-deformation.

Used group $C^*$-algebras and dynamical systems to overcome finite-summability obstructions.

Provided a discrete version of $$-Minkowski deformation.

Abstract

The aim of the paper is to answer the following question: does $\kappa$-deformation 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.