Let K be a field and Γ a finite quiver without oriented cycles. Let Λ := K(Γ,ρ) be the quotient algebra of the path algebra KΓ by the ideal generated by ρ, and let 𝒟(Λ) be the dual extension of Λ. We prove that each Lie derivation of 𝒟(Λ) is of the standard form.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-1-7,
author = {Yanbo Li and Feng Wei},
title = {Lie derivations of dual extensions of algebras},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {65-82},
zbl = {1334.16041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-1-7}
}
Yanbo Li; Feng Wei. Lie derivations of dual extensions of algebras. Colloquium Mathematicae, Tome 139 (2015) pp. 65-82. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-1-7/