DEGENERATIONS FOR SELFINJECTIVE ALGEBRAS OF TREECLASS $D_n$

Abstract

Let $\Lambda$ be a connected representation finite selfinjective algebra. According to $G$ . Zwara the partial orders $\le_{\rm ext}$ and $\le_{\rm deg}$ on the isomorphism classes of $d$ -dimensional $\Lambda$ -modules are equivalent if and only if the stable Auslander–Reiten quiver $\Gamma_{\Lambda}$ of $\Lambda$ is not isomorphic to ${\bb Z}D_{3m}/\tau^{2m-1}$ for all $m\ge 2$ . The paper describes all minimal degenerations $M\le_{\rm deg} N$ with $M\not\leq_{\rm ext} N$ in the case when $\Gamma_\Lambda\cong {\bb Z}D_{3m}/\tau^{2m-1}$ for some $m\ge 2$ .