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Biderivations of triangular algebras

✍ Scribed by Dominik Benkovič

Book ID
104037952
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
214 KB
Volume
431
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let A be a triangular algebra. A bilinear map ϕ : A×A→A is called a biderivation if it is a derivation with respect to both arguments. In this paper we define the concept of an extremal biderivation, and prove that under certain conditions a biderivation of a triangular algebra A is a sum of an extremal and an inner biderivation. The main result is then applied to (block) upper triangular matrix algebras and nest algebras. We also consider the question when a derivation of a triangular algebra is an inner derivation.

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