## Tsukuba Journal of Mathematics

### A Condition for Algebras Associated with a Cyclic Quiver to Be Symmetric

Takashi Teshigawara

#### Abstract

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 $K\Gamma$.

#### Article information

Source
Tsukuba J. Math., Volume 32, Number 1 (2008), 27-35.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496165190

Digital Object Identifier
doi:10.21099/tkbjm/1496165190

Mathematical Reviews number (MathSciNet)
MR2433015

Zentralblatt MATH identifier
1150.16015

#### Citation

Teshigawara, Takashi. A Condition for Algebras Associated with a Cyclic Quiver to Be Symmetric. Tsukuba J. Math. 32 (2008), no. 1, 27--35. doi:10.21099/tkbjm/1496165190. https://projecteuclid.org/euclid.tkbjm/1496165190