论文标题
由投影群集变量生成的群集代数
Cluster algebras generated by projective cluster variables
论文作者
论文摘要
我们介绍了由投影群集变量生成的下界群集代数的概念，该群集变量是在初始群集变量和所谓的投影群集变量上作为多项式环。我们表明，在无循环假设下，群集群集代数和由投影群集变量产生的下限群集代数重合。在这种情况下，我们使用结果为群集代数构建基础。我们还表明，任何类型的$ a_n $或$ \ widetilde {a} _n $的无系数群集代数等于投影群集变量生成的相应下限群集代数。
We introduce the notion of a lower bound cluster algebra generated by projective cluster variables as a polynomial ring over the initial cluster variables and the so-called projective cluster variables. We show that under an acyclicity assumption, the cluster algebra and the lower bound cluster algebra generated by projective cluster variables coincide. In this case we use our results to construct a basis for the cluster algebra. We also show that any coefficient-free cluster algebra of types $A_n$ or $\widetilde{A}_n$ is equal to the corresponding lower bound cluster algebra generated by projective cluster variables.
