Lie triple derivations of incidence algebras

Abstract

Let $\mathcal{R}$ be a 2-torsion free commutative ring with unity, X a locally finite preordered set and $I(X,\mathcal{R})$ the incidence algebra of X over $\mathcal{R}$. If X consists of a finite number of connected components, we prove in this paper that every Lie triple derivation of $I(X,\mathcal{R})$ is proper.

Keywords:

• Derivation
• incidence algebra
• Lie triple derivation

2010 Mathematics Subject Classification:

• Primary 16W25
• Secondary 16W10
• 06A11
• 47L35

Acknowledgments

The authors would like to thank the referees for their valuable comments and suggestions which significantly helped us improve the final presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the NSF of Fujian Province (No. 2018J01002) and the National Natural Science Foundation of China (No. 11301195).