与克罗内克叶理相关的谱三重和微分演算
Spectral triples and differential calculi related to the Kronecker foliation
摘要：
根据Connes和Moscovici的思想，我们描述了两个与Kronecker叶状有关的谱三元组，其广义Dirac算子与一阶和二阶签名算子有关。我们还考虑了相应的微分结石$Ω_D$，这是完全不同的两种情况下。作为边注，我们给出了一个已知的演算的二维非交换环面的生成元和关系的描述。
英文摘要：
Following ideas of Connes and Moscovici, we describe two spectral triples related to the Kronecker foliation, whose generalized Dirac operators are related to first and second order signature operators. We also consider the corresponding differential calculi $Ω_D$, which are drastically different in the two cases. As a side-remark, we give a description of a known calculus on the two-dimensional noncommutative torus in terms of generators and relations.
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