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Elizabeth Henning edited Lusztig_4_Quivers_4_1__.md
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- 4.5 Canonical exact sequence splits (always) iff M ≅ M' ⋆ M''
- In particular, \( V ≅ V(i) ⋆ Φ_i^-Φ_i^+(V) \)
- Corollary: \( Φ_i^-Φ_i^+(V) ≅ V \) iff \( V ∈ M_i^+Ω \)
- The relationship ⋆ is preserved under the equivalence of categories \( M_i^+Ω ≃
M_i^-s_iΩ M^-s_iΩ
- 4.6 Assume i a sink of Ω, V ∈ MΩ indecomposable but not isomorphic to \( e_i \)
- Then \( V ∈ M_i^+Ω \)
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