For a quiver Q of Dynkin type \(\mathbb {A}_{n}\), we give a set of n − 1 inequalities which are necessary and sufficient for a linear stability condition (a.k.a. central charge) \(Z\colon K_{0}(Q) \to \mathbb {C}\) to make all indecomposable representations stable. We furthermore show that these are a minimal set of inequalities defining the space \(\mathcal {T}\mathcal {S}(Q)\) of total stability conditions, considered as an open subset of \(\mathbb {R}^{Q_{0}} \times (\mathbb {R}_{>0})^{Q_{0}}\). We then use these inequalities to show that each fiber of the projection of \(\mathcal {T}\mathcal {S}(Q)\) to \((\mathbb {R}_{>0})^{Q_{0}}\) is linearly equivalent to \(\mathbb {R} \times \mathbb {R}_{>0}^{Q_{1}}\).

对于Dynkin类型\（\ mathbb {A} _ {n} \）的颤动Q，我们给出了n − 1个不等式的集合，这些不等式对于线性稳定性条件（又名中心电荷）\（Z \ colon K_ {0}（Q）\ to \ mathbb {C} \）使所有不可分解的表示稳定。我们进一步证明，这些是定义总稳定性条件的空间\（\ mathcal {T} \ mathcal {S}（Q）\）的最小不等式集合，被视为\（\ mathbb {R} ^的开放子集{Q_ {0}} \ times（\ mathbb {R} _ {> 0}）^ {Q_ {0}} \）。然后，我们使用这些不等式表明\（\ mathcal {T} \ mathcal {S}（Q）\）到\（（\ mathbb {R} _ {> 0}）^ {Q_ { 0}} \）线性等效于\（\ mathbb {R} \ times \ mathbb {R} _ {> 0} ^ {Q_ {1}} \）。