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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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$\mathrm{Ext}$ group in representation theory
Let $\mathcal{X}$ be a finite acyclic quiver, and $v_1$ be a source vertex of $\mathcal{Q}$. Let $\mathcal{X}$ be a representation in $\mathrm{Re}(\mathcal{Q},R)$, where $R$ is a commutative noetheria …
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In quiver rep,is it$\mathrm{Ext}^i_{\mathrm{rep}}(\mathcal{X},\mathcal{R})=0 \leftrightarro...
Let $\mathcal{Q}$ be a finite acyclic quiver, and $R$ be a ring Let $\mathcal{X}$ be a representation in $\mathrm{Rep}(\mathcal{Q},R)$. Let $\mathcal{R}$ represent the image of $R\mathcal{Q}$ under th …