Research for Hilbert C^*-bimodules and associated C^*-algebras

1. 用有限群定义了交叉积C*-双模，得到了一些基本结果。并利用该方法研究了算子代数理论中的A-D对偶问题。这些结果发表在《Hilbert * c -双模在可数离散群上的交叉积》。用有限群上的束定义了交叉积C*-双模，并证明了多重交叉积的结合律。这些结果发表在“Hilbert C*-双模的交叉积”中。研究了C*-代数a上有限生成Hilbert C*-双模相关的C*-代数的理想结构。我们定义了条件(I)并证明了在此条件下的简单性。此外，我们定义了条件（11），并在此条件下给出了双模代数中的理想与a的理想的对应关系，并给出了满足这些条件的一些例子。这些结果发表在“hilbert双模生成的C*-代数的理想结构和简单性”中。用有限群定义了有限生成Hilbert C*-双模上的协同作用。我们证明了所得到的交叉积被制成有限生成的希尔伯特C*双模。这一结果发表在“有限群的Hubert C*-双模的协同交叉积”。定义了以一维环面为分量的可数连续图的Hilbert C*-双模，并研究了相关C*-代数的结构。我们得到了这些代数的简单性和理想结构。这些结果发表在《Hilbert C*-双模与可数无限连续图》6。利用Hilbert C*-双模方法研究奇异动力系统。我们构造了与帐篷图相关的双模的自然基。我们正计划这么做。用我们的方法定义上述动力系统的共轭不变量。

1. We define crossed product C*-bimodule by finite group, and obtain some fundamental results. More-over, we study A-D duality in operator algebra theory by this method. These results are published in "Crossed products of Hilbert *C-bimodules by countable discrete groups".2. We define crossed product C*-bimodule by bundles over finite groups, and prove the associativity law for multiple crossed products. These results are published in "Crossed products of Hilbert C*-bimodule by bundles.3. We investigate ideal structures of C*-algebras associated with finitely generated Hilbert C*-bimodules over unital C*-algebras A.We define the condition (I) and show the simplicity under this condition. Moreover we define the condition (11) and under this condition we present the correspondence the ideals in the bimodules algebras and the ideals of A.We present some examples satisfying these conditions. These results are published in "Ideal structure and simplicity of the C*-algebra generated b9Hilbert bimodules".4. We define coaction on finitely generated Hilbert C*-bimodule by finite groups. We show that resulting crossed product is made into a finitely generated Hilbert C*-bimodule. This results is published in "Coaction crossed products of Hubert C*-bimodule by finite groups".5. We define Hilbert C*-bimodules for countable continuous graphs whose components are 1-dimensional torus, and study the structure of associated C*-algebras. We obtain simplicity and ideal structure of these algebras. These results are published in "Hilbert C*-bimodules and countably infinite continuous graphs"6. We are studying singular dynamical system using Hilbert C*-bimodule method. We construct natural basis for the bimodule associated with the tent map. We are plan to. define conjugacy invariant for the above dynamical systems using our method.