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

作　　者：Zhijie WANG Junyun HU Jiajie HUA 

机构地区：[1]College of Data Science,Jiaxing University,Jiaxing 314001,Zhejiang,China

出　　处：《Chinese Annals of Mathematics,Series B》2023年第4期577-598,共22页数学年刊（B辑英文版）

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)。

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 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*-ALGEBRAS STABILITY Rotation relation UNITARY Flip action 

分 类 号：O15[理学—数学]