论文标题
约旦类型的小零件用于Artinian Gorenstein代数三
Jordan types with small parts for Artinian Gorenstein algebras of codimension three
论文作者
论文摘要
我们研究了具有任意编成的分级Artinian Gorenstein代数的Jordan类型的线性形式。我们介绍了代表各个程度的乘法图等级的线性形式的等级矩阵。我们表明，等级矩阵和约旦度类型之间存在1-1对应关系。对于具有编码三的Artinian Gorenstein代数，我们将所有级别矩阵分类为具有消失的第三功率的线性形式。结果，我们显示了这样的代数表明，最多四个的约旦类型最多由最多三个参数确定。
We study Jordan types of linear forms for graded Artinian Gorenstein algebras having arbitrary codimension. We introduce rank matrices of linear forms for such algebras that represent the ranks of multiplication maps in various degrees. We show that there is a 1-1 correspondence between rank matrices and Jordan degree types. For Artinian Gorenstein algebras with codimension three we classify all rank matrices that occur for linear forms with vanishing third power. As a consequence, we show for such algebras that the possible Jordan types with parts of length at most four are uniquely determined by at most three parameters.
