Gorenstein Graded Algebras and the Evaluation Map

Abstract We consider graded connected Gorenstein algebras with respect to the evaluation map $\text{e}{{\text{v}}_{G\,}}\,=\,\text{Ex}{{\text{t}}_{G}}(k,\varepsilon )\,::\,\text{Ex}{{\text{t}}_{G}}(k,G)\,\to \,\text{Ex}{{\text{t}}_{G}}(k,k)$ . We prove that if $e{{v}_{G}}\,\ne \,0$ , then the global dimension of $G$ is finite.