  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 $n=8$.
