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

作     者：Zhijie WANG Junyun HU Jiajie HUA Zhijie WANG;Junyun HU;Jiajie HUA

作者机构：College of Data ScienceJiaxing UniversityJiaxing 314001ZhejiangChina 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2023年第44卷第4期

页      面：577-598页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China(Nos.11401256,11801219,11501249,11871342) the Scientific Research Fund of Zhejiang Provincial Education Department(No.Y202249575) the Zhejiang Provincial Natural Science Foundation of China(No.LQ13A010016) 

主　　题：C*-Algebras Stability Rotation relation Unitary Flip action 

摘      要：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 anyε0,there existsδ0 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,*** above conclusion is also called that the rotation relations of three unitaries with the flip action is stable under the above conditions.