On Generalized Irrational Rotation Algebras

Wei Sun

2:30 pm to 3:30 pm, May 15th, 2013   Science Building A1510

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.

Inspired by a recent joint work of Junsheng Fang, Chunlan Jiang, Huaxin Lin and Feng Xu, we defined a class of generalized irrational rotation algebras (with the dimension of "zero sets" greater than or equal to $2$), 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 typical crossed product $C^*$-algebras, the tracial spaces and the $K$-theory of such algebras, etc. We also studied the structures of these algebras using results in classification theory of $C^*$-algebras.