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Simple generalized inductive limits of c^(*)-algebras

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Science china Mathematics 2021年第5期64卷 1029-1044页

作者： Xuanlong Fu Department of Mathematics and the Research center for Operator algebras East China Normal UniversityShanghai 200062China

We give a necessary and sufficient condition where a generalized inductive limit becomes a simple c^(*)-algebra. We also show that if a unital c^(*)-algebra can be approximately embedded into some tensorially self absorbing c^(*)-algebra c(e.g., uniformly hyperfinite(UHF)-algebras of infinite type, the cuntz algebra O_(2)),then we can construct a simple separable unital generalized inductive limit. When c is simple and infinite(*** infinite), the construction is also infinite(resp. properly infinite). When c is simple and approximately divisible, the construction is also approximately divisible. When c is a UHF-algebra and the connecting maps satisfy a trace condition, the construction has tracial rank zero.

关键词： c^(*)-algebras generalized inductive limit simplicity approximately divisible tracial rank zero

INHERITANcE OF DIVISIBILITY FORMS A LARGE SUBALGEBRA

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Acta Mathematica Scientia 2021年第1期41卷 85-96页

作者：范庆斋方小春赵霞 Department of Mathematics Shanghai Maritime University Shanghai 201306China Department of Mathematics Tongji University Shanghai 200092China

Let A be an infinite dimensional stably finite unital simple separable c^(*)-*** B■A be a stably(centrally)large subalgebra in A such that B is m-almost divisible(m-almost divisible,weakly(m,n)-divisible).Then A is 2... 详细信息

关键词： c^(*)-algebras large subalgebra cuntz semigroup

On Monotone Product of Operator algebras

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Acta Mathematica Sinica,English Series 2007年第3期23卷 491-496页

作者： Wen Ming WU Li Guang WANG Department of Mathematical Science University of Tsinghua Beijing 100084 P. R. China Department of Mathematics Qufu Normal University Qufu 273165 P. R. China

In this note, we give complete descriptions of the structure of the monotone product of two yon Neumann algebras and two c^＊-algebras. We show that the monotone product of two simple yon Neumann algebras and c^＊-algebras aren＇t simple again. We also show that the monotone product of two hyperfinite yon Neumann algebras is again hyperfinite and determine the type of the monotone product of two factors.

关键词： factor von Neumann algebras monotone product c^*-algebras GNS construction