Equivariant Lorentzian Spectral Triples

2006/11/13 by Paschke, Mario, Andrzej Sitarz, Sitarz, Andrzej · 2 citations
Mathematics · #46L87 #53C50 #58B34 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.math-ph/0611029

openalex publication_date 2006/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present examples of equivariant noncommutative Lorentzian spectral geometries. The equivariance with respect to a compact isometry group (or quantum group) allows to construct the algebraic data of a version of spectral triple geometry adapted to the situation of an indefinite metric. The spectrum of the equivariant Dirac operator is calculated.

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• Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity
• Space and time dimensions of algebras with applications to Lorentzian\n noncommutative geometry and quantum electrodynamics

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