| Abstract: | In the first part of this article, we describe the projective representations in the category of representations by modules of a quiver which does not contain any cycles and the quiver A ∞ as a subquiver, that is, the so-called rooted quivers. As a consequence of this, we show when the category of representations by modules of a quiver admits projective covers. In the second part, we develop a technique involving matrix computations for the quiver A ∞, which will allow us to characterize the projective representations of A ∞. This will improve some previous results and make more accurate the statement made in Benson (1991 Benson , D. J. ( 1991 ). Representations and Cohomology I . Cambridge Studies in Advanced Mathematics , Vol. 30 . Cambridge : Cambridge University Press . [Google Scholar]). We think this technique can be applied in many other general situations to provide information about the decomposition of a projective module. |
