Some prime factorization results for type II<Subscript>1</Subscript> factors期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Some prime factorization results for type II1 factors

Authors:	Narutaka?Ozawa mailto:narutaka@ms.u-tokyo.ac.jp" title=" narutaka@ms.u-tokyo.ac.jp" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Sorin?Popa mailto:popa@math.ucla.edu" title=" popa@math.ucla.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	(1) Department of Mathematical Sciences, University of Tokyo, Komaba, 153-8914, Japan;(2) Department of Mathematics, UCLA, 90095 Los Angeles, CA, USA

Abstract:	We prove several unique prime factorization results for tensor products of type II₁ factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected Lie groups of real rank 1. In particular, we show that if $mathcal{R}overline{otimes}mathcal{L}mathbb{F}_{r_1}overline{otimes}cdotcdotcdotoverline{otimes}mathcal{L}mathbb{F}_{r_m}$ is isomorphic to a subfactor in $mathcal{R}overline{otimes}mathcal{L}mathbb{F}_{s_1}overline{otimes}cdotcdotcdotoverline{otimes}mathcal{L}mathbb{F}_{s_n}$ , for some 2r_i,s_j, then mn. Mathematics Subject Classification (2000) Primary 46L10; Secondary 20F67

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