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arXiv · 1610.01356

Spectral triples on $O_N$

Magnus Goffeng·Bram Mesland
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Abstract

We give a construction of an odd spectral triple on the Cuntz algebra $O_{N}$, whose $K$-homology class generates the odd $K$-homology group $K^1(O_{N})$. Using a metric measure space structure on the Cuntz-Renault groupoid, we introduce a singular integral operator which is the formal analogue of the logarithm of the Laplacian on a Riemannian manifold. Assembling this operator with the infinitesimal generator of the gauge action on $O_{N}$ yields a $\theta$-summable spectral triple whose phase is finitely summable. The relation to previous constructions of Fredholm modules and spectral triples on $O_{N}$ is discussed.

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Magnus Goffeng, Bram Mesland. 2016-10-05. Spectral triples on $O_N$. https://arxiv.org/abs/1610.01356

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