标题： 温和代数上的流 显示英文标题

标题： Flows on Gentle Algebras

摘要： 有向无环图(DAG)上的单位流空间已知可通过DAG的框架诱导出规则单模三角剖分。 充分框架化的DAG及其三角剖分的流多面体最近与某些温和代数的表示理论相关联。 我们通过定义任意温和代数的带边箭图上的流来扩展这种联系。 我们将单位流的空间称为湍流多面体。 我们证明温和代数的支持tau-倾斜模对它的湍流多面体的单模三角剖分进行索引。 在表示无限的情况下，这个三角剖分不是完整的，我们通过向图中添加低维墙给出两种不同的更大的多面体分解。 湍流多面体有一个商映射到我们定义的g-多面体，该多面体位于g-向量扇形的环境空间中，证明了温和代数是g-凸的。 此外，我们两种类型的墙在这个商映射下的像为温和代数的g-向量扇形补集提供了两种不同的解释。 显示英文摘要

摘要： The space of unit flows on a directed acyclic graph (DAG) is known to admit regular unimodular triangulations induced by framings of the DAG. Amply framed DAGs and their triangulated flow polytopes have recently been connected with the representation theory of certain gentle algebras. We expand on this connection by defining a flow on the fringed quiver of an arbitrary gentle algebra. We call the space of unit flows its turbulence polyhedron. We show that support tau-tilting modules of a gentle algebra index a unimodular triangulation of its turbulence polyhedron. In the representation-infinite case, this triangulation is not complete and we give two different larger polyhedral dissections given by adding lower-dimensional walls to the picture. The turbulence polyhedron has a quotient map to what we define as the g-polyhedron lying in the ambient space of the g-vector fan, proving that gentle algebras are g-convex. Moreover, the images of our two types of walls under this quotient map provide two different interpretations for the complement of the g-vector fan of a gentle algebra.