Dimension vector of a quiver representation

Let $𝑊 : Γ ―― \to 𝖥 𝗂 𝗇 𝖵 𝖾 𝖼 𝗍 𝕂$ be a quiver representation. The dimension vector $d i m * 𝑊 \in ℕ Γ 𝑉 0$ of $𝑊$ is the function defined by #m/def/quiv

(d i m * 𝑉) (𝑥) = d i m 𝑉 (𝑥)

where the notation is by analogy to graded dimension. We call any vector in $ℕ Γ 𝑉 0 \subseteq ℚ Γ 𝑉$ a dimension vector for $Γ$ , since one can always

#state/develop | #lang/en | #SemBr