COTORSION REPRESENTATIONS OF QUIVERS

Abstract

It is known that for any quiver Q, the category of representations by modules of Q has enough projectives. An algorithm has been described which provides an easy way for finding a projective representation of a given quiver Q. Furthermore the projective representations obtained by applying this algorithm generate the whole category of representations of Q (see [[3], Section 2]). This fact leads to a characterization of flat representations of Q when Q is a special type of quiver called rooted quiver ([[3], Theorem 3.4]). That characterization was very useful in proving the existence of flat covers for representations of any rooted quiver ([[3], Section 4]), and the existence of flat covers gave the existence of cotorsion envelopes. However, no characterization of cotorsion representations has been given, so the structure of such representations is unknown.

This paper is thus devoted to the characterization of cotorsion representations of quivers. This will be done for every rooted quiver in Theorem 6, where we will see that cotorsion representations are much simpler to describe than flat representations.

Acknowledgments