Jordan (Lie) σ-Derivations on Path Algebras

Abstract

In this paper, we investigate Jordan σ-derivations and Lie σ-derivations on path
algebras. This work is motivated by the one of Benkovic done on triangular algebras
and the study of Jordan derivations and Lie derivations on path algebras done by
Li and Wei. Namely, the main results state that every Jordan σ-derivation is a σ-
derivation and every Lie σ-derivation is of a standard form on a path algebra when
the associated quiver is acyclic and finite.