 Tits form of a quiver

The quadratic form is $q_Q(\mathbf{n})=⟨\mathbf{n},\mathbf{n}{⟩}_Q={\sum }_i{n}_i^2-{\sum }_{\rho :i\to j}{n}_i{n}_j$. It depends on the underlying graph rather than its orientation. For a representation it equals $\dim {\mathrm{End}}_Q(X)-\dim {\mathrm{Ext}}_Q^1(X,X)$. Its positive definiteness forces indecomposables to be rigid brick modules, using the Ringel lemma on bricks.