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arXiv · 2010.10091

Quadratic algebras associated with exterior 3-forms

Michel Dubois-Violette·Blas Torrecillas
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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 $n$ 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 $n=8$.

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Michel Dubois-Violette, Blas Torrecillas. 2020-10-20. Quadratic algebras associated with exterior 3-forms. https://arxiv.org/abs/2010.10091

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