Let $K$ be a field, $f(x)$ a monic polynomial in $K[x]$ and $KG$ the path algebra of a cyclic quiver $G$ with $s$ vertices and $s$ arrows. In this paper, we give a necessary and sufficient condition for the algebra $K\Gamma/(f(X))$ to be a symmetric algebra, where $X$ is the sum of all arrows in $K\Gamma$.
Takashi Teshigawara. "A Condition for Algebras Associated with a Cyclic Quiver to Be Symmetric." Tsukuba J. Math. 32 (1) 27 - 35, June 2008. https://doi.org/10.21099/tkbjm/1496165190