Nonlinear Lie derivations of incidence algebras

Abstract

Let (X , ) be a locally finite preordered set and R a 2-torsion free commutative ring with unity, I(X ,R) the incidence algebra of X over R . In this paper, we give an explicit description of the structure of nonlinear Lie derivations of I(X ,R) . We prove that every nonlinear Lie derivation of I(X ,R) is a sum of an inner derivation, a transitive induced derivation and an additive induced Lie derivation. Mathematics subject classification (2010): Primary 16S40, 16W25; Secondary 16G20, 06A11, 47L35.