论文标题
与对称常规超电势相关的非交通锥分类的分类
Classification of noncommutative conics associated to symmetric regular superpotentials
论文作者
论文摘要
令$ s $为$ 3 $维量子多项式代数，而在s_2 $中的$ f \是中心常规元素。商代数$ a = s/（f）$称为非交通锥。对于非交换性圆锥$ a $，有一个有限的维数代数$ c（a）$，它决定了$ a $的奇异性。在本文中，我们主要专注于非交通圆锥，使其二级二元二元相当，相当于说，$ s $由对称的常规超电势决定。我们将这些非交通性锥体分类为对$（s，f）$的同构，并计算代数$ c（a）$。
Let $S$ be a $3$-dimensional quantum polynomial algebra, and $f \in S_2$ a central regular element. The quotient algebra $A = S/(f)$ is called a noncommutative conic. For a noncommutative conic $A$, there is a finite dimensional algebra $C(A)$ which determines the singularity of $A$. In this paper, we mainly focus on a noncommutative conic such that its quadratic dual is commutative, which is equivalent to say, $S$ is determined by a symmetric regular superpotential. We classify these noncommutative conics up to isomorphism of the pairs $(S,f)$, and calculate the algebras $C(A)$.
