Jordan derivations and antiderivations on triangular matrices

By Dominik Benkovič. 2005

84 citations recorded by the source corpus.

Abstract We define an antiderivation from an algebra A into an A -bimodule M as a linear map δ : A → M such that δ(ab) = δ(b)a + bδ(a) for all a , b ∈ A . The main result states that every Jordan derivation from the algebra of all upper triangular matrices into its bimodule is the sum of a derivation and an antiderivation.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8bf3bb845ed72d7810edb4b8663899561fd458ad

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Characterizations of derivations and Jordan derivations on Banach algebras (2009, background): “However, there exist continuous Jordan derivationswhich are not derivations [1,2,8].”
On Jordan Derivations of Triangular Algebras (2007, background): “But the inverse, in general, is not true (see [1]).”
Jordan derivations of triangular algebras (2006, background): “The converse is, in general, not true (see [3]).”