Spectral triples for higher-rank graph $C^*$-algebras
| Autor: | Judith A. Packer, Elizabeth Gillaspy, Sooran Kang, Carla Farsi, Antoine Julien |
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| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Strongly connected component Pure mathematics 46L05 46L87 58J42 Mathematics::Operator Algebras General Mathematics Mathematics - Operator Algebras Matematikk: 410 [VDP] Dirac operator Noncommutative geometry Graph Mathematics: 410 [VDP] symbols.namesake Wavelet decomposition Differential Geometry (math.DG) FOS: Mathematics symbols Path space Operator Algebras (math.OA) Spectral triple Brownian motion Mathematics |
| Zdroj: | Mathematica Scandinavica |
| ISSN: | 1903-1807 0025-5521 |
| DOI: | 10.7146/math.scand.a-119260 |
| Popis: | In this note, we present a new way to associate a spectral triple to the noncommutative $C^*$-algebra $C^*(\Lambda)$ of a strongly connected finite higher-rank graph $\Lambda$. We generalize a spectral triple of Consani and Marcolli from Cuntz-Krieger algebras to higher-rank graph $C^*$-algebras $C^*(\Lambda)$, and we prove that these spectral triples are intimately connected to the wavelet decomposition of the infinite path space of $\Lambda$ which was introduced by Farsi, Gillaspy, Kang, and Packer in 2015. In particular, we prove that the wavelet decomposition of Farsi et al. describes the eigenspaces of the Dirac operator of this spectral triple. Comment: This paper is a partial replacement of arXiv:1701.05321; the latter will not be submitted for publication |
| Databáze: | OpenAIRE |
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