Lie derivations of dual extensions of algebras
Volume 141 / 2015
Colloquium Mathematicum 141 (2015), 65-82
MSC: 16W25, 16G20, 15A78.
DOI: 10.4064/cm141-1-7
Abstract
Let $K$ be a field and $\varGamma $ a finite quiver without oriented cycles. Let $\varLambda :=K(\varGamma , \rho )$ be the quotient algebra of the path algebra $K\varGamma $ by the ideal generated by $\rho $, and let $\mathscr {D}(\varLambda )$ be the dual extension of $\varLambda $. We prove that each Lie derivation of $\mathscr {D}(\varLambda )$ is of the standard form.
