报告人简介

Masaki Izumi（泉正己），现任京都大学理学研究科教授。泉正己教授在算子代数、尤其是次因子理论领域的工作闻名遐迩。他给出了很多一般方法无法完成的具体范例的构造，并以出色的技巧给出了各种各样完整的计算。其主要结果为：对指数4以下次因子分类理论的贡献及其在指数5以下情况的进一步推广、量子二重构造法的具体计算、Haagerup次因子的新型构造及其推广、古典Galois理论的量子化版本以及其次因子方面的结果在C*-代数的子代数研究领域的类比。

泉正己教授于1996年获得日本数学会赏建部贤弘赏，2003年获得日本数学会解析学赏，2004年获得作用素环赏（这是日本国内算子代数领域的最高奖项），2010年获得日本数学会秋季赏（这相当于日本国内的沃尔夫奖），2010年受邀做ICM报告，2014年获得井上学术赏。

内容简介

The notion of qausi-product actions of a compact group on a C*-algebra was introduced by Bratteli et al. in their attempt to seek an equivariant analogue of Glimm's characterization of non-type I C*-algebras. We show that a faithful minimal action of a second countable compact group on a separable C*-algebra is quasi-product whenever its fixed point algebra is simple. This was previously known only for compact abelian groups and for profinite groups. Our proof relies on a subfactor technique applied to finite index inclusions of simple C*-algebras in the purely infinite case, and also uses ergodic actions of compact groups in the general case. As an application, we show that if moreover the fixed point algebra is a Kirchberg algebra, such an action is always isometrically shift-absorbing, and hence is classifiable by the equivariant KK-theory due to a recent result of Gabe-Szabó.