Quiver representation

Dimension vector of a quiver representation

Let 𝑊 :Γ―― →𝖥𝗂𝗇𝖵𝖾𝖼𝗍𝕂 be a quiver representation. The dimension vector dim∗⁡𝑊 ∈ℕΓ𝑉0 of 𝑊 is the function defined by quiv

(dim∗⁡𝑉)(𝑥)=dim⁡𝑉(𝑥)

where the notation is by analogy to graded dimension. We call any vector in ℕΓ𝑉0 ⊆ℚΓ𝑉 a dimension vector for Γ, since one can always

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