Study of operator algebras and dynamical systems from various perspectives

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400108
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Chiba University
• Principal Investigator: Matui Hiroki 千葉大学, 大学院理学研究院, 教授 (40345012)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 作用素環 / 極小力学系

Outline of Final Research Achievements

I studied operator algebras and dynamical systems from various perspectives. In particular, I focused on classification of group actions on simple nuclear C*-algebras and analysis of minimal dynamical systems on Cantor sets. For instance, I obtained a complete classification of outer actions of poly-Z-groups on Kirchberg algebras up to cocycle conjugacy. Secondly, I classified etale groupoids arising from finite products of shifts of finite type, and computed the homology groups of the etale groupoids and the abelianizations of the associated topological full groups.

Free Research Field

作用素環論