论文标题
与外部3型相关的二次代数
Quadratic algebras associated with exterior 3-forms
论文作者
论文摘要
本文致力于研究二次代数的研究，其关系是外部3型的超电势产生的。这样的代数是规律的，并且仅当它是koszul，而是一个3-卡拉比YAU域。经过一些一般结果，我们调查了以低维度$ n $生成的代数的情况，其中$ n \ leq 7 $。我们表明，每当基地闭合地面磁场时，所有这些代数与3个规则外部3型相关的代数是规则的，因此是3-喀拉比YAU结构域。此结果不会概括为尺寸$ n $，其中$ n \ geq 8 $：我们描述了一个尺寸$ n = 8 $的反示例。
This paper is devoted to the study of the quadratic algebras with relations generated by superpotentials which are exterior 3-forms. Such an algebra is regular if and only if it is Koszul and is then a 3-Calabi-Yau domain. After some general results we investigate the case of the algebras generated in low dimensions $n$ with $n\leq 7$. We show that whenever the ground field is algebraically closed all these algebras associated with 3-regular exterior 3-forms are regular and are thus 3-Calabi-Yau domains. This result does not generalize to dimensions $n$ with $n\geq 8$ : we describe a counter example in dimension $n=8$.
