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Lusztig §4 - Quivers  - 4.1 For a Dynkin quiver $ Ω $, Ω,  denote by MΩ the (abelian) category of modules (representations) over a fixed field F - 4.2 Any simple module is isomorphic to some \( e_i ≔ V_i = F, V_j = 0 \)  [link](https://www.authorea.com/users/97602/articles/116277/_show_article#article-paragraph-mobile__space__test__dot__md)  - 4.3 Full subcategories \( M_i^+Ω \) and \( M_i^-Ω \) characterized by Hom