A lifting problem for DG modules

Maiko Ono and Yuji Yoshino

Let $B=A ¥langle X
dX=t¥rangle$ 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 $Ext^{n+1}_B(N,N)=0$. Furthermore such a lifting is unique up to DG isomorphisms if $Ext^n_B(N,N)=0$.

Journal of Algebra

Elsevier, Inc.

556

342

360