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"Quiver" is the word used for "directed graph" in some parts of representation theory. The main reason to use the term quiver is to indicate an interest in considering representations of the quiver.
5
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When is a given quiver algebra a hopf algebra?
The paper "algebres de chemin quantiques" by Cibils and Rosso answers exactely that question. Adv in Math 125(2) 1997