Compact $\kappa$-deformation and spectral triples

Abstract

We construct discrete versions of $\kappa$-Minkowski space related to a certain compactness of the time coordinate. We show that these models fit into the framework of noncommutative geometry in the sense of spectral triples. The dynamical system of the underlying discrete groups (which include some Baumslag--Solitar groups) is heavily 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. The dimension of these spectral triples is unrelated to the number of coordinates defining the $\kappa$-deformed Minkowski spaces.

30 pages

References in corpus (6)

• 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
• A no-pure-boost uncertainty principle from spacetime noncommutativity
• kappa-Minkowski representations on Hilbert spaces
• Spectral triples and the super-Virasoro algebra
• First results of the Noether theorem for Hopf-algebra spacetime symmetries
• On the 5D differential calculus and translation transformations in 4D kappa-Minkowski noncommutative spacetime

Cited by in corpus (3)

• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• A modular spectral triple for $\kappa$-Minkowski space
• Testing Noncommutative Spacetimes and Violations of the Pauli Exclusion Principle with underground experiments