A bimodule approach to the strong no loop conjecture

Let A be a finite-dimensional elementary k-algebra, where k is a field. For B a finite-dimensional k-algebra, the Hattori–Stallings trace is studied at the level of projective B-modules that are A–B-bimodules. A bimodule characterization of the projective dimension of a simple A-module is provided. These results are applied to give an alternative proof of Igusa–Liu–Paquette Theorem, i.e., the strong no loop conjecture for finite-dimensional elementary k-algebras.