论文标题
驯服代数有密集$ \ mathbf {g} $ - 矢量粉丝
Tame algebras have dense $\mathbf{g}$-vector fans
论文作者
论文摘要
$ \ mathbf {g} $ - 有限维代数的矢量粉丝是粉丝的粉丝，其射线是其$ 2 $ - term presilting对象的$ \ mathbf {g} $ - 矢量。我们证明$ \ mathbf {g} $ - 驯服代数的矢量迷是密集的。然后，我们将此结果应用于近乎分类的Quivers分类，用于使用jacobian代数的集群代数的添加剂分类，用于群集$ \ mathbf {g} $ - 矢量风扇是密度或半空间的。作为另一种应用，我们证明，对于曾经由曾经插入的闭合表面产生的电势的颤动，稳定性和簇散射图仅通过在分离超平面中包含的墙壁上的墙壁交叉功能而有所不同。附录致力于构造截断的扭曲函数及其伴随。
The $\mathbf{g}$-vector fan of a finite-dimensional algebra is a fan whose rays are the $\mathbf{g}$-vectors of its $2$-term presilting objects. We prove that the $\mathbf{g}$-vector fan of a tame algebra is dense. We then apply this result to obtain a near classification of quivers for which the closure of the cluster $\mathbf{g}$-vector fan is dense or is a half-space, using the additive categorification of cluster algebras by means of Jacobian algebras. As another application, we prove that for quivers with potentials arising from once-punctured closed surfaces, the stability and cluster scattering diagrams only differ by wall-crossing functions on the walls contained in a separating hyperplane. The appendix is devoted to the construction of truncated twist functors and their adjoints.
