Let $B = A $ be an extended DG algebra by the adjunction of variable of positive even degree $n$, and let $N$ be a semi-free DG $B$-module that is assumed to be bounded below as a graded module. We prove in this paper that $N$ is liftable to $A$ if $Ext_B^{n+1}(N,N)=0$. Furthermore such a lifting is unique up to DG isomorphisms if $Ext_B^{n}(N,N)=0$.

中文翻译：

---

DG 模块的吊装问题

令 $B = A $ 是由正偶数 $n$ 的变量附加的扩展 DG 代数，并令 $N$ 是一个半自由的 DG $B$-模模块。我们在本文中证明，如果 $Ext_B^{n+1}(N,N)=0$，$N$ 可以提升到 $A$。此外，如果 $Ext_B^{n}(N,N)=0$，则这种提升对于 DG 同构来说是唯一的。