Ringel form
= Ringel form
{c}
{title2=$\langle\mathbf n,\mathbf m\rangle_Q$}
= Euler form of a quiver
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{synonym}
This bilinear form is $\langle\mathbf n,\mathbf m\rangle_Q=\sum_i n_im_i-\sum_{\rho:i\to j}n_im_j$. The <standard projective resolution of a quiver representation> gives its value as $\dim\operatorname{Hom}_Q(X,Y)-\dim\operatorname{Ext}^1_Q(X,Y)$ for the dimension vectors of $X,Y$. Its diagonal is the <Tits form of a quiver>.