Tits form of a quiver
= Tits form of a quiver
{c}
{title2=$q_Q(\mathbf n)$}
The quadratic form is $q_Q(\mathbf n)=\langle\mathbf n,\mathbf n\rangle_Q=\sum_i n_i^2-\sum_{\rho:i\to j}n_in_j$. It depends on the underlying graph rather than its orientation. For a representation it equals $\dim\operatorname{End}_Q(X)-\dim\operatorname{Ext}^1_Q(X,X)$. Its positive definiteness forces indecomposables to be rigid <brick modules>, using the <Ringel lemma on bricks>.