Yoneda algebras of almost Koszul algebras

摘要

Let e?‘? be an algebraically closed field, e??′ a finite dimensional connected (e?‘?, e?‘?)-Koszul self-injective algebra with e?‘?, e?‘? a‰￥ 2. In this paper, we prove that the Yoneda algebra of e??′ is isomorphic to a twisted polynomial algebra $A^!$ [e?‘? ; e???] in one indeterminate e?‘? of degree e?‘?+1 in which $A^!$ is the quadratic dual of e??′, e??? is an automorphism of $A^!$, and e?‘?e?‘? = e???(e?‘?)e?‘? for each $t in A^!$. As a corollary, we recover Theorem 5.3 of [2].