Generalized Lie derivations on triangular algebras

• Published in: Linear algebra and its applications Vol. 434; no. 6; pp. 1532 - 1544
• Main Author: BENKOVIC, Dominik
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 15.03.2011; Elsevier
• Subjects: Algebra; Associative rings and algebras; Exact sciences and technology; Generalized derivation; Generalized Jordan derivation; Generalized Lie derivation; Linear and multilinear algebra, matrix theory; Mathematical analysis; Mathematics; Nest algebra; Operator theory; Sciences and techniques of general use; Triangular algebra; Triangular matrix algebra; Generalized Jordan derivation; Nest algebra; 15A78; Generalized derivation; Triangular matrix algebra; 16W25; Generalized Lie derivation; 16R60; 47L35; Triangular algebra; Triangular matrix; Matrix algebra; Operator algebra; Upper triangular matrix; Jordan algebra; Bimodule; Ring; Lie group; Lie algebra; Block matrix
• ISSN: 0024-3795; 1873-1856
• DOI: 10.1016/j.laa.2010.11.039

Let A be a unital algebra and let M be a unitary A -bimodule. We consider generalized Lie derivations mapping from A to M . Our results are applied to triangular algebras, in particular to nest algebras and (block) upper triangular matrix algebras. We prove that under certain conditions each generalized Lie derivation of a triangular algebra A is the sum of a generalized derivation and a central map which vanishes on all commutators of A .