On the properties of the exchange graph of a cluster algebra
On the properties of the exchange graph of a cluster algebra
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DOI：
10.4310/mrl.2008.v15.n2.a10
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发表时间：
2007-03
影响因子：
1
通讯作者：
M. Gekhtman;M. Shapiro;A. Vainshtein
中科院分区：
文献类型：
--
作者：
M. Gekhtman;M. Shapiro;A. Vainshtein
在两种情况下证明了关于簇代数$\A$的交换图的点和边的猜想：当$\A$是几何型的和当$\A$是任意的且其交换矩阵是非退化的.在第二种情况下，我们还证明了交换图不依赖于$\A$的系数。这两种理论都是最近由Fomin和Zelevinsky提出的。
We prove a conjecture about the vertices and edges of the exchange graph of a cluster algebra $\A$ in two cases: when $\A$ is of geometric type and when $\A$ is arbitrary and its exchange matrix is nondegenerate. In the second case we also prove that the exchange graph does not depend on the coefficients of $\A$. Both conjectures were formulated recently by Fomin and Zelevinsky.