Jordan代数上的三元映射

设A和B是Jordan代数, 如果双射:A→B满足任给a,b,c∈A都有(｛abc｝)=｛(a)(b)(c)｝, 则称为Jordan三元映射。如果A含有一个非平凡幂等p,且A对于p的Peirce分解A=A1A12A0满足(1)设ai∈Ai(i=1,0),如果任给t12∈A12都有ait12=0,则ai=0,则从A到B上的Jordan三元映射是可加的。

Multiplicative Jordan triple isomorphisms on Jordan algebras

Let A and B be Jordan algebra. The bijection :A→B is called a Jordan triple map, if (｛abc｝)=｛(a)(b)(c)｝JP] for all a,b,c∈A. IfA　contains a non trivial idempotent p, and the Peirce decomposition A=A₁A₁₂,A₀  of  A with respect to p, and satisfies that(1) ai∈Ai(i=1,0), if ait₁₂=0 for all t₁₂∈A12, then   a _i=0, every Jordan triple map from A onto B is additive.