Lie derivations on triangular matrices

Author: Benkovic˘, Dominik

Source: Linear and Multilinear Algebra, Volume 55, Number 6, November 2007 , pp. 619-626(8)

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Abstract:

Let [image omitted] be the algebra of all n × n upper triangular matrices over a commutative unital ring [image omitted], and let [image omitted] be a 2-torsion free unital [image omitted]-bimodule. We show that every Lie derivation [image omitted] is a sum of a derivation and a linear map having its range in the center of [image omitted]. We also consider the question of innerness of derivations from [image omitted] into [image omitted].

Keywords: Triangular matrix algebra; Lie derivation; Derivation; 2000 Mathematics Subject Classifications; 16W10; 15A04; 17B40

Document Type: Research article

DOI: http://dx.doi.org/10.1080/03081080701379107

Affiliations: 1: University of Maribor, 2000 Maribor, Slovenia

Publication date: 2007-11-01