A characterization of quiver algebras based on double derivations

TL;DR

This paper characterizes finite quiver algebras over a characteristic zero field using double derivations, providing a non-commutative analogue of Wright's classical result.

Contribution

It introduces a new characterization of quiver algebras via double derivations, extending classical results to the non-commutative setting.

Findings

Algebras with suitable double derivations are isomorphic to quiver algebras.

Provides a non-commutative version of Wright's characterization.

Establishes conditions under which an algebra is a quiver algebra.

Abstract

Let k a characteristic zero field. We give a characterization for the finite quiver k-algebras, based on double derivations. More precisely, we prove that if an associative and unitary k-algebra have a family of double derivations satisfying suitable conditions, then it is (canonically isomorphic to) a quiver algebra. This is the non-commutative version of a result of D. Wright.