Details of talk
|Title||The injective Leavitt complex|
|Presenter||Huanhuan Li (University of Western Sydney)|
|Author(s)||Dr Huanhuan Li|
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.