特征为2的素^(*)-代数上强保持2-新积

Strong 2-new product preserving maps on prime-algebras of characteristic 2

设R是特征为2包含非平凡对称幂等元的单位素*-代数.对A,B∈R,定义A·B=AB+BA*为新积,(A·B)_(2)=(A·(A·B))为2-新积。设φ:R→R是满射.对所有A,B∈R,如果φ满足(φ(A)·φ(B))_(2)=(A·B)_(2)当且仅当对所有A∈R,存在α∈C_(s)且α^(3)=I使得φ(A)=αA,其中I是R的单位,C_(s)是R的对称可延拓中心.作为应用,得到了索C*代数和因子von Neumann代数上保持上述性质映射的结构.

Let R be a unital prime *-algebra of characteristic 2 containing a nontrivial symmetric idempotent.For A,B ∈R,the new product and 2-new product are defined,respectively,by A·B=AB+BA* and(A·B)2=(A·(A·B)).Let φ:R→R be a surjective map.It is shown that φ satisfies(φ(A)·φ(B))2=(A·B)_(2) for all A,B∈R if and only if there exists α∈C_(S) with α3=I such that φ(A)=aA for all A∈R,where C_(S) is the symmetric extend centroid of R.As an application,such maps on prime C* algebras and factor von Neumann algebras are characterized.