低维度量子透镜空间的等变同构

Søren Eilers, Sophie Emma Zegers
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引用次数: 0

摘要

量子透镜空间构成了一类自然的、研究得很透彻的非交换空间,利用已发展的图$C^*$-数组的分类理论,我们用代数变量对其进行了部分分类。我们引入了两个量子透镜空间等变同构的问题,并在某些基本情况下求解了这个问题。结果可以直接用定义量子透镜空间的参数来表述,这里偶尔会出现一个相当复杂的问题,这让我们相信我们的发现有一个深刻的内在解释。我们用计算实验来补充完全确定的部分结果,这些实验可能会指明前进的方向。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Equivariant isomorphism of Quantum Lens Spaces of low dimension
The quantum lens spaces form a natural and well-studied class of noncommutative spaces which has been partially classified using algebraic invariants drawing on the developed classification theory of graph $C^*$-algebras. We introduce the problem of deciding when two quantum lens spaces are equivariantly isomorphic, and solve it in certain basic cases. The results can be formulated directly in terms of the parameters defining the quantum lens spaces, and here occasionally take on a rather complicated from which convinces us that there is a deep underlying explanation for our findings. We complement the fully established partial results with computer experiments that may indicate the way forward.
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