The Injective Leavitt Complex

• DOI: 10.1007/s10468-017-9741-9
• Publication Date: 2017-10-13T07:02:39Z
• Authors: Huanhuan Li
• Keywords: Quiver; Zero (linguistics)

23 pages<br/>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.<br/>