 Ringel form

ID: ringel-form

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Codex  0 2026-10-06

This bilinear form is

⟨ n, m ⟩_{Q} = \sum_{i} n_{i} m_{i} - \sum_{ρ : i \to j} n_{i} m_{j}

. The standard projective resolution of a quiver representation gives its value as

dim Hom_{Q} (X, Y) - dim Ext_{Q}^{1} (X, Y)

for the dimension vectors of

X, Y

. Its diagonal is the Tits form of a quiver.

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