Study of group actions on operator algebras

算子代数群作用的研究

• 批准号: 22740099
• 负责人: MATUI HIROKI
• 金额: $ 2.58万
• 依托单位: Chiba University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22740099/
• 关键词: 作用素環; 群作用; 極小力学系; K理論; 軌道同型

I studied group actions on operator algebras and related topics. In particular, I focused on simple nuclear C*-algebras, which can be thought of as non-commutative topological spaces. First, various group actions on simple nuclear C*-algebras were classified up to cocycle conjugacy. For instance, uniqueness of actions of finitely generated free abelian groups on UHF algebras of infinite type was obtained. Secondly, it was proved that a large class of simple nuclear C*-algebras are classified by their K-groups. Also, I showed that topological full groups associated with minimal dynamical systems have various interesting properties.

我研究了算子代数和相关主题的群行动。我特别关注简单的核 C* 代数，它可以被认为是非交换拓扑空间。首先，简单核 C* 代数上的各种群作用被分类为余循环共轭。例如，获得了有限生成的自由阿贝尔群在无限型UHF代数上的唯一性。其次，证明了一大类简单核C*代数可以通过它们的K群来分类。此外，我还表明与最小动力系统相关的拓扑完整群具有各种有趣的属性。

项目成果

Recent progress in classification of simple C*-algebras

简单 C* 代数分类的最新进展

• 发表时间: 2013
• 作者: Inou;Hiroyuki;H. Matui
• 通讯作者: H. Matui

Some remarks on topological full groups of Cantor minimal systems II

关于康托极小系统II的拓扑满群的一些评论

• DOI: 10.1017/s0143385712000399
• 发表时间: 2013
• 期刊: Ergodic Theory Dynam. Systems
• 作者: Hiroshi Takeda;Shuji Yoshikawa;野邊厚;H. Matui
• 通讯作者: H. Matui

Strict comparison and Z-absorption of nuclear C*-algebras

• 发表时间: 2011-11
• 期刊: arXiv: Operator Algebras
• 作者: H. Matui;Yasuhiko Sato

Classification of Z^N-actions on simple C^*-algebras

简单 C^* 代数上的 Z^N 动作分类

• 发表时间: 2010
• 作者: University Gadjah Mada;Yogyakarta;Indonesia;Hiroyuki Inou;柴山允瑠;K. Svadlenka;稲生啓行;Hiroyuki Inou;有田親史;松井宏樹;Svadlenka Karel;稲生 啓行;柴山允瑠;稲生啓行;柴山允瑠;H. Matui;野邊厚;Hiroyuki Inou;H.Matui;野邊厚;Hiroyuki Inou;野邊厚;野邊厚;Hiroyuki Inou;K. Svadlenka;野邊厚;Hiroyuki Inou;M. Shibayama;H. Matui;野邊厚;稲生 啓行;M. Shibayama;H.Matui
• 通讯作者: H.Matui

Z^N-actions on UHF algebras of infinite type

• 发表时间: 2010-04
• 期刊: arXiv: Operator Algebras
• 作者: H. Matui