A complete classification of 3-dimensional quadratic AS-regular algebras of Type EC

2019/12/11 by Masaki Matsuno, Matsuno, Masaki
Mathematics · #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1912.05167

18 pages

arxiv created 2019/12/16 · arxiv updated 2019/12/17

Abstract

Classification of AS-regular algebras is one of the main interests in noncommutative algebraic geometry. We say that a 3-dimensional quadratic AS-regular algebra is of Type EC if its point scheme is an elliptic curve in ℙ². In this paper, we give a complete list of geometric pairs and a complete list of twisted superpotentials corresponding to such algebras. As an application, we show that there are only two exceptions up to isomorphism among all 3-dimensional quadratic AS-regular algebras which cannot be written as a twist of a Calabi-Yau AS-regular algebra by a graded algebra automorphism.

Related

• Classifications of 3-dimensional cubic AS-regular algebras whose point schemes are not integral
• Defining relations of 3-dimensional cubic AS-regular algebras of Type P, S and T
• Exotic Elliptic Algebras of dimension 4 (with an Appendix by Derek Tomlin)
• Twisted algebras of geometric algebras
• Quadratic algebras associated with exterior 3-forms