Classifying local Artinian Gorenstein algebras

详细信息    查看全文

• 作者：Joachim Jelisiejew
• 关键词：Mathematics Subject ClassificationPrimary 13H10 ; Secondary 13N10 ; 14C05
• 刊名：Collectanea Mathematica
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：68
• 期：1
• 页码：101-127
• 全文大小：651KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics; Algebra; Geometry; Analysis;
• 出版者：Springer Milan
• ISSN：2038-4815
• 卷排序：68

文摘

The classification of local Artinian Gorenstein algebras is equivalent to the study of orbits of a certain non-reductive group action on a polynomial ring. We give an explicit formula for the orbits and their tangent spaces. We apply our technique to analyse when an algebra is isomorphic to its associated graded algebra. We classify algebras with Hilbert function (1, 3, 3, 3, 1), obtaining finitely many isomorphism types, and those with Hilbert function (1, 2, 2, 2, 1, 1, 1). We consider fields of arbitrary, large enough, characteristic.