论文标题
用lefschetz属性分解单一代数
On decomposing monomial algebras with the Lefschetz properties
论文作者
论文摘要
我们引入了一种用于分解单一代数的通用技术，用于研究Lefschetz属性。我们将技术应用于各种代数，包括单一几乎完整的交叉点和戈伦斯坦代数。特别是，我们证明了戈伦斯坦编码三个代数由数值半群引起的代数具有强大的lefschetz特性。我们还研究了分裂操作的相反 - 胶合操作 - 它提供了一种构建具有lefschetz属性的单一代数的方法。
We introduce a general technique for decomposing monomial algebras which we use to study the Lefschetz properties. We apply our technique to various classes of algebras, including monomial almost complete intersections and Gorenstein algebras. In particular, we prove that Gorenstein codimension three algebras arising from numerical semigroups have the strong Lefschetz property. We also study the reverse of the splitting operation -- a gluing operation -- which gives a way to construct monomial algebras with the Lefschetz properties.
