Automorphisms of operator algebras and quantum measures

算子代数和量子测度的自同构

基本信息

批准号：
10640199
负责人：
SAITO Kazuyuki
金额：
$ 0.77万
依托单位：
Tohoku University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640199/
关键词：
automorphisms von Neumann algebras monotone complete C^*-algebras AFD-factors outer automorphisms operator algebras C^*-algebras quantum measures 因子環 C^*_- 環

项目摘要

We showed that when M is a von Neumann algebra with a non atomic center then an easy argument can be given to establish the boundedness of completely additive quantum measures ou M.In particular, if {n_j} is a sequence of positive integers and, for each j, A_j ia an abelian von Neumann algebra. with no minimal projections, and M_j is the algebra of n_j by n_j matrices then Σ_j【symmetry】(M_j 【cross product】A_j) is a von Neumann algebra not covered by the Dorofeev-Shertsnev theorem but one to which our results apply. By combining the results obtained here with their deep theorems (specialized to factors) the best possible result is obtained.Let M be a von Neumann algebra which does not have any direct summand isomorphic to the algebra of n by n matrices (for n an integer greater than 1). Then every completely additive quantum measure on M is bounded.2. Let B be any monotone complete C^*-algebra and let G be any locally compact separable Hausdorff group. We gave necessary and sufficient c … More onditions on the (B, G) for the existence of an action α of G on B as a group of *-automorphisms in such a way that (B, G, α) is an admissible dynamical system. Roughly, it is a monotone complete C^*-dynamical system (B, G, α) for which we can construct a monotone complete cross-product B x_α G with the canonical embedding of B.Furthermore, when G is abelian, we can define a dual action of G in such a way that the duality principle of Takesaki is valid.3. We constructed non-trivial examples of admissible monotone complete C^*-dynamic systems. In particular, we constructed such a system where G is the additive group R of real numbers or the Torus T, and where B is the Generic Dynamics Factor A.4. Let Out(A) = Aut(A)/Inn(A) be the outer automorphism group of A.Then, for each integer p with p 【greater than or equal】 2 and each complex number γ with γ^p=1, we constructed periodic automorphisms of A with Connes' outer conjugacy invariant (p, γ) of outer periodicity.5. For any countable discrete group G, it is shown that G can be isomorphically embedded in Out(A). Less

我们表明，如果{n_j}是一个正整数的序列，而对于每个J，对于每个J，A_J A_J a_j a abelian von neumann代数而没有最小的预测，则在带有肛门原子中心的代数时，aasy参数尤其可以量子。 ] a_j）是von neumann代数，由dorofeev- shertsnev therich therich therich我们的结果适用。直接汇总N矩阵的n代数（对于n个整数），然后在MET上进行了cuantum。在这种（B，G，G，α）中，（B，G，α）在（B，G，α）的AROUP上的存在（B，G）上有更多的拥有。 B.Furthermore，当G是Abelian时，我们可以定义Takeaki的双重动作。 g是A. t的良好组或圆环。，表明g可以嵌入到out（a）中