Jordan derivations on block upper triangular matrix algebras

TL;DR

This paper characterizes Jordan derivations on block upper triangular matrix algebras, showing they can be decomposed into derivations and antiderivations, thus advancing understanding of their algebraic structure.

Contribution

It proves that any Jordan derivation on these algebras can be expressed as a sum of a derivation and an antiderivation, providing a new structural insight.

Findings

Jordan derivations decompose into derivations and antiderivations

Applicable to block upper triangular matrix algebras over complex numbers

Enhances understanding of algebraic derivation structures

Abstract

We provide that any Jordan derivation from the block upper triangular matrix algebra $\T = \T(n_{1},n_{2}, \cdots, n_{k})\subseteq M_{n}(\mathbb{\C})$ into a $2$-torsion free unital $\T$-bimodule is the sum of a derivation and an antiderivation.