  For a finite quiver $Q$ without sinks, we consider the corresponding finite
dimensional algebra $A$ with radical square zero. We construct an explicit
compact generator for the homotopy category of acyclic complexes of injective
$A$-modules. We call such a generator the injective Leavitt complex of $Q$.
This terminology is justified by the following result: the differential graded
endomorphism algebra of the injective Leavitt complex of $Q$ is
quasi-isomorphic to the Leavitt path algebra of $Q$. Here, the Leavitt path
algebra is naturally Z-graded and viewed as a differential graded algebra with
trivial differential.
