Generalized Lie triple derivations on generalized matrix algebras

Abstract

Let $\mathcal{R}$ be a commutative ring with identity, $\mathcal{A},\mathcal{B}$ be $\mathcal{R}$-algebras, $\mathcal{M}$ be an $(\mathcal{A},\mathcal{B})$-bimodule and $\mathcal{N}$ be a $(\mathcal{B},\mathcal{A})$-bimodule. The $\mathcal{R}$-algebra $\mathcal{G}=G(\mathcal{A},\mathcal{M},\mathcal{N},\mathcal{B})$ is a generalized matrix algebra defined by the Morita context $(\mathcal{A},\mathcal{B},\mathcal{M},\mathcal{N},{\zeta }_{\mathcal{M}\mathcal{N}},{\chi }_{\mathcal{N}\mathcal{M}}).$ In this article, we give the structure of generalized Lie triple derivations G_L on generalized matrix algebras $\mathcal{G}$ and prove that under certain restrictions G_L can be written as $G_L=\Delta +\chi ,$ where Δ is a generalized derivation and χ is a central valued mapping.

Keywords:

• Generalized derivation
• generalized Lie derivation
• generalized Lie triple derivation
• generalized matrix algebra

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16W25
• 15A78
• 47L35

Acknowledgement

The authors are indebted to the referee for his/her helpful comments and suggestions which have improved the article.

Additional information

Funding

The second author is partially supported by a research grant from NBHM (No. 02011/5/2020 NBHM(R.P.) R&D II/6243).