Classification of noncommutative conics associated to symmetric regular superpotentials.

Let S be a 3 -dimensional quantum polynomial algebra, and f ∈ 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). [ABSTRACT FROM AUTHOR]