On spectral triples on crossed products arising from equicontinuous actions
On spectral triples on crossed products arising from equicontinuous actions
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DOI：
10.7146/math.scand.a-15572
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发表时间：
2011-03
期刊：
影响因子：
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通讯作者：
Andrew Hawkins;Adam G. Skalski;Stuart White;J. Zacharias
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文献类型：
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作者：
Andrew Hawkins;Adam G. Skalski;Stuart White;J. Zacharias
利用外Kasparov积通过自然意义上等度连续的离散群的作用，构造了$C^*-代数的交叉积上的奇、偶谱三元组。对于Belissard，Marcoli和Reihani提出的谱三元组，当这个群是$\Z$时，这给出了另一种观点。我们研究了这种结构的性质，并利用它产生了由Cantor集上的里程计作用和AF-代数的其他一些交叉积产生的Bunce-Dedden代数上的谱三元组。
The external Kasparov product is used to construct odd and even spectral triples on crossed products of $C^*$-algebras by actions of discrete groups which are equicontinuous in a natural sense. When the group in question is $\Z$ this gives another viewpoint on the spectral triples introduced by Belissard, Marcolli and Reihani. We investigate the properties of this construction and apply it to produce spectral triples on the Bunce-Deddens algebra arising from the odometer action on the Cantor set and some other crossed products of AF-algebras.