Biderivations of triangular algebras
Biderivations of triangular algebras
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DOI：
10.1016/j.laa.2009.05.029
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发表时间：
2009-10
影响因子：
1.1
通讯作者：
Dominik Benkovič
中科院分区：
文献类型：
--
作者：
Dominik Benkovič
设A是一个三角代数.一个双线性映射φ：A×A→A称为双导子，如果它是关于两个变元的导子。本文定义了极值双导数的概念，证明了在一定条件下三角代数A的双导数是极值双导数与内双导数之和。主要结果，然后适用于（块）上三角矩阵代数和套代数。我们还考虑了三角代数的导子是内导子的问题。
Let A be a triangular algebra. A bilinear map φ:A×A→A is called a biderivation if it is a derivation with respect to both arguments. In this paper we define the concept of an extremal biderivation, and prove that under certain conditions a biderivation of a triangular algebra A is a sum of an extremal and an inner biderivation. The main result is then applied to (block) upper triangular matrix algebras and nest algebras. We also consider the question when a derivation of a triangular algebra is an inner derivation.