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Lie derivations of triangular algebras. (English) Zbl 1060.16033
Under rather mild technical conditions it is shown that every Lie derivation of a triangular algebra is of standard form, i.e., it is a sum of a derivation and a map with range in the center. This result is applied to some special triangular algebras, for example to triangular matrix algebras and to nest algebras.

16W25 Derivations, actions of Lie algebras
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
16S50 Endomorphism rings; matrix rings
15A78 Other algebras built from modules
17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
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