论文标题
在与常规Polyhedra面部姿势相关的Artinian Gorenstein代数上
On Artinian Gorenstein algebras associated to the face posets of regular polyhedra
论文作者
论文摘要
我们介绍了由普通Polyhedra的脸部定义的Artinian Gorenstein代数。我们考虑了代数的强大左手属性和杂物 - 居民关系。我们显示了所有柏拉图固体的代数的强级左手。另一方面，对于某些柏拉图固体，我们表明代数不满足与某些较强的Lefschetz元素相对于Riemann的关系。
We introduce Artinian Gorenstein algebras defined by the face posets of regular polyhedra. We consider the strong Lefschetz property and Hodge--Riemann relation for the algebras. We show the strong Lefschetz property of the algebras for all Platonic solids. On the other hand, for some Platonic solids, we show that the algebras do not satisfy the Hodge--Riemann relation with respect to some strong Lefschetz elements.
