A lifting problem for DG modules

Abstract

Let $B=A<X|dX=t>$ 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 $Ex{t}_B^{n+1}(N,N)=0$. Furthermore such a lifting is unique up to DG isomorphisms if $Ex{t}_B^n(N,N)=0$.

17 pages