Multiplicative Lie n-derivations of triangular rings

• Published in: Linear algebra and its applications Vol. 436; no. 11; pp. 4223 - 4240
• Main Authors: Benkovič, Dominik, Eremita, Daniel
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.06.2012; Elsevier
• Subjects: Algebra; Associative rings and algebras; Derivation; Exact sciences and technology; Lie derivation; Lie triple derivation; Linear and multilinear algebra, matrix theory; Mathematical analysis; Mathematics; Multiplicative Lie n-derivation; Nest algebra; Operator theory; Sciences and techniques of general use; Triangular ring; Upper triangular matrix ring; Lie derivation; Lie triple derivation; Nest algebra; 15A78; Derivation; 16W25; Upper triangular matrix ring; Multiplicative Lie n-derivation; 47L35; Triangular ring; Operator algebra; Upper triangular matrix; Ring; Lie group; Block matrix
• ISSN: 0024-3795; 1873-1856
• DOI: 10.1016/j.laa.2012.01.022

We introduce the notion of a multiplicative Lie n-derivation of a ring, generalizing the notion of a Lie (triple) derivation. The main goal of the paper is to consider the question of when do all multiplicative Lie n-derivations of a triangular ring T have the so-called standard form. The main result is applied to the classical examples of triangular rings: nest algebras and (block) upper triangular matrix rings.