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Stability of Rotation Relations of Three Unitaries with the Flip Action in c^(*)C*-algebras

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chinese Annals of Mathematics,Series B 2023年第4期44卷 577-598页

作者： Zhijie WANG Junyun HU Jiajie HUA college of Data Science Jiaxing UniversityJiaxing 314001ZhejiangChina

The authors show that ifΘ=(θ_(jk))is a 3×3 totally irrational real skewsymmetric matrix,whereθ_(jk)∈[0,1)for j,k=1,2,3,then for anyε>0,there existsδ>0 satisfying the following:For any unital c^(*)-algebra A with the cancellation property,strict comparison and nonempty tracial state space,any four unitaries u1,u2,u3,w∈A such that(1)■,wujw-1=uj-1,w2=1A for j,k=1,2,3;(2)τ(aw)=0 and■for all n∈N,all a∈c^(*)(u1,u2,u3),j,k=1,2,3 and all tracial statesτon A,where c^(*)(u1,u2,u3)is the c^(*)-subalgebra generated by u1,u2 and u3,there exists a 4-tuple of unitaries■in A such that■and■for j,k=1,2,3.The above conclusion is also called that the rotation relations of three unitaries with the flip action is stable under the above conditions.

关键词： c*C*-algebras Stability Rotation relation Unitary Flip action

certain cuntz Semigroup Properties of certain crossed Product c^*C*-algebras

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Acta Mathematica Sinica,English Series 2020年第3期36卷 337-362页

作者： Qing Zhai FAN Department of Mathematics Shanghai Maritime UniversityShanghai 201306P.R.C hina

We show that the following properties of the c^*C*-algebras in a class Ω are inherited by simple unital C*-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an application,let A be an infinite dimensional simple unital c-algebra such that A has one of the above-listed properties.Suppose that α:G→Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property.Then the crossed product c^*-algebra c^*(G,A,α) also has the property under consideration.

关键词： c^*C*-algebras tracial approximation cuntz semigroup

Simple generalized inductive limits of c^(*)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)C*-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(resp.properly 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^(*)C*-algebras generalized inductive limit simplicity approximately divisible tracial rank zero

Property T^(**) for c~*C*-algebras

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Acta Mathematica Sinica,English Series 2012年第9期28卷 1845-1850页

作者： Dan LI chern Institute of Mathematics Nankai University

Extending the notion of property T of finite von Neumann algebras to general yon Neu- mann algebras, we define and study in this paper property T＊＊ for （possibly non-unital） c＊C*-algebras. We obtain several results of property T＊＊ parallel to those of property T for unital c＊C*-algebras. Moreover, we show that a discrete group F has property T if and only if the group c＊-algebra c＊（F）（or equivalently, the reduced group c＊-algebra c＊（F）） has property T＊＊. We also show that the compact operators K（g2） has property T＊＊ but co does not have property T＊＊.

关键词： Property T＊＊ c＊C*-algebras Hilbert bimodules

A class of c^(*)C*-algebras with Non-stable K_1-Group Property

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Acta Mathematica Sinica,English Series 2012年第5期28卷 983-988页

作者： Qing Zhai FAN Xiao chun FANG Department of Mathematics Shanghai Maritime University Department of Mathematics Tongji University

In this paper, we give a class of c＊C*-algebras with non-stable K1-group property which include the example non-simple tracial topological rank zero and stable rank two c＊-algebra given by Lin and Osaka.

关键词： c＊C*-algebras stable rank non-stable

Some Results on Inner Quasidiagonal c^*C*-algebras

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Acta Mathematica Sinica,English Series 2020年第10期36卷 1094-1106页

作者： Qi Hui LI Rui WANG School of Science East China University of Science and TechnologyShanghai 200237P.R.China Shanghai Aerospace control Technology Institute Shanghai 200211P.R.Chin

In the current article,we prove the crossed product c^*-algebra by a Rokhlin action of finite group on a strongly quasidiagonal c^*-algebra is strongly quasidiagonal again.We also show that a just-infinite c^*-algebra is quasidiagonal if and only if it is inner quasidiagonal.Finally,we compute the topological free entropy dimension in just-infinite c^*C*-algebras.

关键词： Inner quasidiagonal c*C*-algebras crossed product c*C*-algebras strongly quasidiagonal c^*C*-algebras just-infinite c^*C*-algebras topological free entropy dimension

Proof of inseparable prime c~*C*-algebras A with RR(A)=0 being primitive c~*C*-algebras

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chinese Science Bulletin 1999年第8期44卷 688-690页

作者： ZHANG Lunchuan and MA JipuDepartment of Mathematics , Beijing Normal University , Beijing 100875, china Department of Mathematics , Nanjing University, Nanjing 210093, china Department of Mathematics Beijing Normal University Beijing China Department of Mathematics Nanjing University Nanjing China

First, that prime c~* C*-algebras with countable primitive ideals are all primitive c*C*-algebras is proved. Then the proof that prime c~* C*-algebras with property RR(A) = 0 are all primitive c~*C*-algebras is given.

关键词： prime c~*C*-algebras primitive c~*C*-algebras hereditary c~*C*-algebras open projection and close projection.

cOMPLETELY POSITIVE MAPS AND-ISOMORPHISM OF C*-algebras

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chinese Annals of Mathematics 1988年第1期 27-31页

作者：吴良森 Department of Mathematics East china Normal University Shanghai china.

Let A,B be unital c*C*-algebras.XA={|are all completely positive linear maps from Mn（c）to A with ‖a‖≤1}.(a=((e11)…(e1n……(en1)…(enn)),where{eiy}is the matrix unit of Mn（c）.)Let a be the natural action of SU（n）on Mn（c）.For n≥3,if Φis an a-invariant affine isomorphism between XA and XB,Φ（0）=0,then A and B are*-isomorphic.In this paper a counter example is given for the case n=2.

关键词： cOMPLETELY POSITIVE MAPS AND-ISOMORPHISM OF C*-algebras view 二拍

A Bishop-Stone-Weierstrass Theorem for (M_2(c))~n

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Acta Mathematica Sinica,English Series 2013年第8期29卷 1515-1534页

作者： Qi Hui LI Don HADWIN Department of Mathematics East China University of Science and Technology Department of Mathematics and Statistics University of New Hampshire

In this paper, we shall give an elementary proof of a Bishop–Stone–Weierstrass theorem for （M2（c））n with respect to its pure states. To be more precise, we shall show that the pure-state Bishop hull of a unital ... 详细信息

关键词： Bishop–Stone–Weierstrass theorem pure states c＊C*-algebras