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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.

MSC:
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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