Examples of infinite direct sums of spectral triples

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• 作者：Kevin Falk ; ^{kevin-falk@hotmail.com}
• 关键词：Noncommutative geometry ; Spectral triples ; Toeplitz operators ; Self-similar sets
• 刊名：Journal of Geometry and Physics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：112
• 期：Complete
• 页码：240-251
• 全文大小：524 K
• 卷排序：112

文摘

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 CnCn. Secondly, we construct a spectral triple associated to a general polygonal self-similar set in CC using algebras of Toeplitz operators on Hardy spaces. In this case, we show that we can recover the Hausdorff dimension of the fractal set.