Quadratic algebras associated with exterior 3-forms

Fuente: arXiv
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Main Authors: Dubois-Violette, Michel, Torrecillas, Blas
Format: Preprint
Published: 2020
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author Dubois-Violette, Michel
Torrecillas, Blas
author_facet Dubois-Violette, Michel
Torrecillas, Blas
contents 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 $n=8$.
format Preprint
id arxiv_https___arxiv_org_abs_2010_10091
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Quadratic algebras associated with exterior 3-forms
Dubois-Violette, Michel
Torrecillas, Blas
Rings and Algebras
Quantum Algebra
15, 16
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 $n=8$.
title Quadratic algebras associated with exterior 3-forms
topic Rings and Algebras
Quantum Algebra
15, 16
url https://arxiv.org/abs/2010.10091