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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.12737 |
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| _version_ | 1866914839215996928 |
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| author | Chandler, R. G. Tran, H. Veerapen, P. Wang, X. |
| author_facet | Chandler, R. G. Tran, H. Veerapen, P. Wang, X. |
| contents | In this paper, we classify connected graded quadratic Artin-Schelter regular (AS-regular, henceforth) algebras of global dimension four that have a Hilbert series the same as that of the polynomial ring on four generators and that map onto a twisted homogeneous coordinate ring of a rank-two quadric. A twisted homogeneous coordinate ring is a construction that was defined by Artin, Tate, and Van den Bergh in \cite{ATV1, ATV2, AVdB1990} in the context of the classification of AS-regular algebras of global dimension three. In \cite{SV99,VVr}, the authors classified AS-regular algebras of global dimension four that map onto the twisted homogeneous coordinate ring of a rank-three and a rank-four quadric, respectively. We expand on their work to include the case of coordinate rings of a rank-two quadric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12737 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regular algebras of dimension four associated to coordinate rings of rank-two quadrics Chandler, R. G. Tran, H. Veerapen, P. Wang, X. Rings and Algebras 14A22, 16S37, 16S38 In this paper, we classify connected graded quadratic Artin-Schelter regular (AS-regular, henceforth) algebras of global dimension four that have a Hilbert series the same as that of the polynomial ring on four generators and that map onto a twisted homogeneous coordinate ring of a rank-two quadric. A twisted homogeneous coordinate ring is a construction that was defined by Artin, Tate, and Van den Bergh in \cite{ATV1, ATV2, AVdB1990} in the context of the classification of AS-regular algebras of global dimension three. In \cite{SV99,VVr}, the authors classified AS-regular algebras of global dimension four that map onto the twisted homogeneous coordinate ring of a rank-three and a rank-four quadric, respectively. We expand on their work to include the case of coordinate rings of a rank-two quadric. |
| title | Regular algebras of dimension four associated to coordinate rings of rank-two quadrics |
| topic | Rings and Algebras 14A22, 16S37, 16S38 |
| url | https://arxiv.org/abs/2406.12737 |