Lie n-derivations of incidence algebras

Abstract

Let n be a positive integer with $n\ge 2.$ Let X be a locally finite preordered set, R a commutative ring with unity and I(X, R) the incidence algebra of X over R. We prove in this article that every Lie n-derivation of I(X, R) is proper provided that R is 2-torsion free and $(n-1)$-torsion free, which gives a positive answer for a conjecture by Wang and Xiao. see [Lie triple derivations of incidence algebras. Commun. Algebra, 47(5): 1841-1852.]

Keywords:

• Derivation
• incidence algebra
• Lie n-derivation

2010 Mathematics Subject Classification:

• Primary 16W25, Secondary 06A11, 16G20, 47L35

Additional information

Funding

The first author is supported by the NSF of Fujian Province (No. 2018J01002). The second author is supported in part by the NSFC (No. 11701468) and Southwest University (No. XDJK2017C052).