三角代数上的零点ξ-Lie可导映射

ξ-Lie derivable maps at zero point on triangular algebras

研究了三角代数上的零点ξ-Lie可导映射,证明了三角代数U上的每一个零点ξ-Lie(ξ≠1)可导映射δ都具有形式T→d(T)+δ(I)T,其中d:U→U是一个可加导子.作为应用,得到:上三角块矩阵代数T上的零点ξ-Lie(ξ≠1)可导映射具有形式T→TS-ST+Td+λT,其中S∈T,λ∈F,d是F上的可加导子且Td=(d(tij));套代数AlgN上的零点ξ-Lie(ξ≠1)可导映射具有形式T→TS-ST+λT,其中S∈AlgN,λ∈F.

The maps on triangular algebras which are ξ-Lie derivable at zero are disscussed.It is proved that every map δ on a triangular algebra U which is ξ-Lie derivable at zero with ξ≠1 has the form T→d（T）＋δ（I）T,where d：U→U is an additive derivation.As applications,it is shown that a map on the upper triangular block matrix algebra T which is ξ-Lie derivable at zero with ξ≠1 has the form T→TS-ST＋Td＋λT,where S∈T,λ∈F,d is an additive derivation and Td=（d（tij））;a map on the nest algebra Alg N which is ξ-Lie derivable at zero with ξ≠1 has the form T→TS-ST＋λT,where S∈Alg N,λ∈F.