## Tsukuba Journal of Mathematics

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

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

#### 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

**Permanent link to this document**

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