Quadratic algebras associated with exterior 3-forms
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866913186109718528 |
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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 |
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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 |