Quadratic algebras associated with exterior 3-forms

  • Michel Dubois-Violette

    Université Paris-Saclay, Orsay, France
  • Blas Torrecillas

    Universidad de Almeria, Spain
Quadratic algebras associated with exterior 3-forms cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

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 with . 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 with : we describe a counterexample in dimension .

Cite this article

Michel Dubois-Violette, Blas Torrecillas, Quadratic algebras associated with exterior 3-forms. J. Noncommut. Geom. 19 (2025), no. 4, pp. 1515–1543

DOI 10.4171/JNCG/586