A generalized Yoneda algebra of an algebra associated with a cyclic quiver

Abstract

Let $A=K\text{Γ}/(X^k)$, where $K\text{Γ}$ is the path algebra of a cyclic quiver $\text{Γ}$ over a field $K,X$ is the sum of all arrows of $\text{Γ}$ and $k$ is a positive integer. In this paper, we describe the ring structure of the generalized Yoneda algebra ${\oplus }_{i\ge 0}{\text{Ext}}_A^i(A/J^l,A/J^l)$ of $A$ with multiplication given by the Yoneda product, where $J$ denotes the Jacobson radical of $A$ and $l$ is a positive integer with $l\le k$.