设U=Tri(A,M,B)是一个三角代数,其中A和B是实数域或复数域F上含单位元的代数,M是一个忠实的左A-模和忠实的右B模,ξ≠0,1.本文证明了U上每个ξ-Lie可乘双射Φ(即Φ(AB-ξBA)=Φ(A)Φ(B)-ξΦ(B)Φ(A)对所有的A,B∈U均成立)都是ξ-Lie环同构.作为应用,得到上三角块矩阵代数和套代数上ξ-Lie可乘双射的完全刻画.

Let U = Tri(A,M,B) be a triangular algebra,where A and B are unital algebras over a real or complex field F,and M is a faithful left A-module as well as a faithful right B-module.Forξ≠0,1,we show that everyξ-Lie multiplicative bijective mapΦ:U→U is additive and thus aξ-Lie ring isomorphism.As applications,ξ-Lie multiplicative bijective maps on upper triangular block matrix algebras and Banach space nest algebras are characterized completely.