Tuesday, July 23, 14:00, 7.527
Huanhuan Li (Western Sydney University), The injective Leavitt complex.
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.