A bimodule approach to the strong no loop conjecture

Yang Han ^[1]
1. [1] Chinese Academy of Sciences
  
  Chinese Academy of Sciences
  
  China
Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 6 (June 2015), 2015, págs. 2139-2143
Idioma: inglés
DOI: 10.1016/j.jpaa.2014.07.028
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Resumen
- 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.