報(bào)告人簡(jiǎn)介
Masaki Izumi（泉正己），現(xiàn)任京都大學(xué)理學(xué)研究科教授。泉正己教授在算子代數(shù)、尤其是次因子理論領(lǐng)域的工作聞名遐邇。他給出了很多一般方法無(wú)法完成的具體范例的構(gòu)造，并以出色的技巧給出了各種各樣完整的計(jì)算。其主要結(jié)果為：對(duì)指數(shù)4以下次因子分類(lèi)理論的貢獻(xiàn)及其在指數(shù)5以下情況的進(jìn)一步推廣、量子二重構(gòu)造法的具體計(jì)算、Haagerup次因子的新型構(gòu)造及其推廣、古典Galois理論的量子化版本以及其次因子方面的結(jié)果在C*-代數(shù)的子代數(shù)研究領(lǐng)域的類(lèi)比。
泉正己教授于1996年獲得日本數(shù)學(xué)會(huì)賞建部賢弘賞，2003年獲得日本數(shù)學(xué)會(huì)解析學(xué)賞，2004年獲得作用素環(huán)賞（這是日本國(guó)內(nèi)算子代數(shù)領(lǐng)域的最高獎(jiǎng)項(xiàng)），2010年獲得日本數(shù)學(xué)會(huì)秋季賞（這相當(dāng)于日本國(guó)內(nèi)的沃爾夫獎(jiǎng)），2010年受邀做ICM報(bào)告，2014年獲得井上學(xué)術(shù)賞。
內(nèi)容簡(jiǎn)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.
