TY - JOUR
AU - Carla Farsi
AU - Elizabeth Gillaspy
AU - Antoine Julien
AU - Sooran Kang
AU - Judith Packer
PY - 2020/05/06
Y2 - 2020/06/05
TI - Spectral triples for higher-rank graph $C^*$-algebras
JF - MATHEMATICA SCANDINAVICA
JA - MathScand
VL - 126
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-119260
UR - https://www.mscand.dk/article/view/119260
AB - 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 Λ. Our spectral triple builds on an approach used by Consani and Marcolli to construct spectral triples for Cuntz-Krieger algebras. We prove that our spectral triples are intimately connected to the wavelet decomposition of the infinite path space of Λ 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 our spectral triple. The paper concludes by discussing other properties of the spectral triple, namely, θ-summability and Brownian motion.
ER -