Derived equivalences of DG algebras are not governed by their cohomology rings

Abstract

Let $\mathcal{A}$ and $\mathcal{B}$ be two connected cochain DG algebra such that ${\mathcal{A}}^{\#}={\mathcal{B}}^{\#}$ and the cohomology rings $H(\mathcal{A})$ and $H(\mathcal{B})$ are isomorphic. We give examples to show that $\mathcal{A}$ and $\mathcal{B}$ are not necessarily derived equivalent, thereby answering to a question of Dugas.

20 pages