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Article Dans Une Revue Journal of Geometry and Physics Année : 2017

Examples of infinite direct sums of spectral triples

Résumé

We study two ways of summing an infinite family of noncommutative spectral triples. First, we propose a definition of the integration of spectral triples and give an example using algebras of Toeplitz operators acting on weighted Bergman spaces over the unit ball of $\mathbb{C}^n$. Secondly, we construct a spectral triple associated to a general polygonal self-similar set in $\mathbb{C}$ using algebras of Toeplitz operators on Hardy spaces. In this case, we show that we can recover the Hausdorff dimension of the fractal set.
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hal-01696562 , version 1 (24-04-2018)

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Kevin Falk. Examples of infinite direct sums of spectral triples. Journal of Geometry and Physics, 2017, 112, pp.240 - 251. ⟨10.1016/j.geomphys.2016.10.019⟩. ⟨hal-01696562⟩
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