Huanhuan Li (Western Sydney University), The injective Leavitt complex.

Abstract:

For a finite graph E 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 E. This terminology is justified by the following result: the differential graded endomorphism algebra of the injective Leavitt complex of E is quasi-isomorphic to the Leavitt path algebra of E. Here, the Leavitt path algebra is naturally Z-graded and viewed as a differential graded algebra with trivial differential.