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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.
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Projective resolution of a quiver with relations
How do we compute the projective resolution of a representation of a quiver with relations.
For example consider the Beilinson quiver $B_4$
$.
with the relations $\{\alpha_j^k\alpha_i^{k-1}=\alpha_i^ …