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Lie derivations on triangular matrices. (English) Zbl 1129.16024
Let \(T_n(C)\) be the algebra of all \(n\times n\) upper triangular matrices over a commutative unital ring \(C\). The main result shows that every Lie derivation from \(T_n(C)\) into a 2-torsion free unital \(T_n(C)\)-bimodule \(M\) is of a standard form, i.e., it is a sum of a derivation and a linear map having its range in the center of \(M\). Some remarks concerning the innerness of derivations from \(T_n(C)\) into \(M\) are also given.

MSC:
16W25 Derivations, actions of Lie algebras
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
16S50 Endomorphism rings; matrix rings
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