$\kappa$-Deformation and Spectral Triples

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 $C^{\ast }$-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.

Talk presented by B. Iochum at the conference "Geometry and Physics in Cracow", September 21-25, 2010

References in corpus (5)

• A no-pure-boost uncertainty principle from spacetime noncommutativity
• Spectral triples and the super-Virasoro algebra
• First results of the Noether theorem for Hopf-algebra spacetime symmetries
• A class of $C^{\ast }$-algebras generalizing both graph algebras and homeomorphism $C^{\ast }$-algebras IV, pure infiniteness
• Circle correspondence $C^{\ast }$-algebras

Cited by in corpus (3)

• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• K-theory for the $C^{\ast }$-algebras of the solvable Baumslag-Solitar groups