For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system （A, G, α）, G<sub>α</sub><sup>×</sup> A =...For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system （A, G, α）, G<sub>α</sub><sup>×</sup> A = G<sub>αγ</sub><sup>×</sup> A, if G is amenable. About the inverse, few discussions have been seen.展开更多
Let （A, Z, α） be a C<sup>*</sup>-dynamical system, and α<sup>n</sup>=id （n is a fixed positive integer）. A natural problem is how the C<sup>*</sup>-crossed product A ×<...Let （A, Z, α） be a C<sup>*</sup>-dynamical system, and α<sup>n</sup>=id （n is a fixed positive integer）. A natural problem is how the C<sup>*</sup>-crossed product A ×<sub>α</sub>Z relates to A×<sub>α</sub>Z<sub>n</sub>. The answer is the following: A×<sub>α</sub>Z≌M<sub>A×<sub>α</sub>Z<sub>n</sub></sub>,where M<sub>A×<sub>α</sub>Z<sub>n</sub></sub> is the mapping torus of , and （A×<sub>α</sub>Z<sub>n</sub>, <sub>n</sub>, ）is the dual system展开更多
In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of SU(2), U(2), SO(3), SO(3)×S^(1) and Spin ^(C)(3). We defin...In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of SU(2), U(2), SO(3), SO(3)×S^(1) and Spin ^(C)(3). We define the rotation vectors(numbers) of the left actions induced by the elements in the maximal tori of these groups, and utilize rotation vectors(numbers) to give the topologically conjugate classification of the left actions. Algebraic conjugacy and smooth conjugacy are also considered. As a by-product, we show that for any homeomorphism f : L(p,-1) × S^(1)→ L(p,-1) × S^(1), the induced isomorphism(π■f■i)_(*) maps each element in the fundamental group of L(p,-1) to itself or its inverse, where i : L(p,-1) → L(p,-1) × S^(1) is the natural inclusion and π : L(p,-1) × S^(1)→ L(p,-1) is the projection.展开更多
文摘For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system （A, G, α）, G<sub>α</sub><sup>×</sup> A = G<sub>αγ</sub><sup>×</sup> A, if G is amenable. About the inverse, few discussions have been seen.
基金Project partially supported by the National Natural Science Foundation of China.
文摘Let （A, Z, α） be a C<sup>*</sup>-dynamical system, and α<sup>n</sup>=id （n is a fixed positive integer）. A natural problem is how the C<sup>*</sup>-crossed product A ×<sub>α</sub>Z relates to A×<sub>α</sub>Z<sub>n</sub>. The answer is the following: A×<sub>α</sub>Z≌M<sub>A×<sub>α</sub>Z<sub>n</sub></sub>,where M<sub>A×<sub>α</sub>Z<sub>n</sub></sub> is the mapping torus of , and （A×<sub>α</sub>Z<sub>n</sub>, <sub>n</sub>, ）is the dual system
文摘In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of SU(2), U(2), SO(3), SO(3)×S^(1) and Spin ^(C)(3). We define the rotation vectors(numbers) of the left actions induced by the elements in the maximal tori of these groups, and utilize rotation vectors(numbers) to give the topologically conjugate classification of the left actions. Algebraic conjugacy and smooth conjugacy are also considered. As a by-product, we show that for any homeomorphism f : L(p,-1) × S^(1)→ L(p,-1) × S^(1), the induced isomorphism(π■f■i)_(*) maps each element in the fundamental group of L(p,-1) to itself or its inverse, where i : L(p,-1) → L(p,-1) × S^(1) is the natural inclusion and π : L(p,-1) × S^(1)→ L(p,-1) is the projection.
