低维量子透镜空间上的等变同构

摘要(中文译文)

量子透镜空间构成了一类自然且研究充分的非交换空间，借助已臻完善的单位图C*-代数分类理论，可通过代数不变量对其进行分类。我们提出了判定两个量子透镜空间何时等变同构的问题，并在若干基本情形下予以解决。与同构分类不同，在等变情形下我们无法诉诸一个完整的一般分类理论，但通过将现有部分结果与针对性分析相结合，我们能够完全解决维度为3的情形，并在素情形下解决维度为5的情形。我们的结果可以直接用定义量子透镜空间的参数来表述，而在此处有时会呈现出相当复杂的形式，这使我们确信我们的发现背后存在深层的根本解释。我们以计算机实验补充了已完全确立的部分结果，这些实验可能指示前进的方向。

Abstract

The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph -algebras. We introduce the problem of deciding when two quantum lens spaces are equivariantly isomorphic, and solve it in certain basic cases. As opposed to classification up to isomorphism, we can not appeal to a complete general classification theory in the equivariant case, but by combining existing partial results with an ad hoc analysis we can solve the case with dimension 3 completely, and the case with dimension 5 in the prime case. Our results can be formulated directly in terms of the parameters defining the quantum lens spaces, and here occasionally take on a rather complicated form 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.

如何引用