Examples of infinite direct sums of spectral triples
arXiv:1602.07458 · doi:10.1016/j.geomphys.2016.10.019
Abstract
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 . Secondly, we construct a spectral triple associated to a general polygonal self-similar set in using algebras of Toeplitz operators on Hardy spaces. In this case, we show that we can recover the Hausdorff dimension of the fractal set.
16 pages