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On Generalized Irrational Rotation Algebras
孙伟(华东师范大学)
2018-01-01 12:13  华东师范大学

青年学术论坛报告

摘要: 无理旋转代数(或者更一般的,非交换环面)是非交换几何中非常经典的例子。过去的数十年里,关于其结构的研究涉及到了拓扑动力系统,叉积C*代数等领域。 关于其结构的典型结果之一就是:所有的单的非交换环面(无论其维数多大)都是AT代数。 我们试图定义了广义的无理旋转代数。作为一类广义的非交换环面,我们应用最新的C*代数分类理论来研究其K理论,进而给出了相应的结构描述。



Abstract:

Irrational Rotation Algebras had been typical examples of noncommutative geometry, which can be regarded as a class of noncommutative torus. They also have their roots in crossed product C*-algebras, and their structures have been studied with the developments of classification theory for nuclear simple C*-algebras.

We defined a class of generalized irrational rotation algebras, which covers the standard case but has more freedom in the sense of generators. We studied the relationship between the generalized irrational rotation algebras and crossed product C*-algebras, the tracial spaces of such algebras, the K-theory of them, etc. We also studied the structures of these algebras using results in classification theory of C*-algebras.