论文标题
几何类型的广义群集代数
On the Generalized Cluster Algebras of Geometric Type
论文作者
论文摘要
我们开发并证明了[Berenstein A.，Fomin S.，Zelevinsky A.，Duke Math所示的一些结果的类似物。 J. 126（2005），1-52]关于群集代数的下限和上限与几何类型的广义群集代数。我们表明，在无效和共同点的条件下，下限与上限一致。因此，我们获得了这些广义群集代数的标准单基础。此外，在附录中，我们证明一个无循环的群集代数等于相应的广义上群集代数，而没有假设存在共同点。
We develop and prove the analogs of some results shown in [Berenstein A., Fomin S., Zelevinsky A., Duke Math. J. 126 (2005), 1-52] concerning lower and upper bounds of cluster algebras to the generalized cluster algebras of geometric type. We show that lower bounds coincide with upper bounds under the conditions of acyclicity and coprimality. Consequently, we obtain the standard monomial bases of these generalized cluster algebras. Moreover, in the appendix, we prove that an acyclic generalized cluster algebra is equal to the corresponding generalized upper cluster algebra without the assumption of the existence of coprimality.
