ID | 60866 |
フルテキストURL | |
著者 |
Itaba, Ayako
Department of Mathematics, faculty of Science, Tokyo University of Science
Matsuno, Masaki
Graduate School of Science and Technology, Shizuoka University
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抄録 | Classification of AS-regular algebras is one of the main interests in non-commutative algebraic geometry. Recently, a complete list of superpotentials (defining relations) of all 3-dimensional AS-regular algebras which are Calabi-Yau was given by Mori-Smith (the quadratic case) and Mori-Ueyama (the cubic case), however, no complete list of defining relations of all 3-dimensional AS-regular algebras has not appeared in the literature. In this paper, we give all possible defining relations of 3-dimensional quadratic AS-regular algebras. Moreover, we classify them up to isomorphism and up to graded Morita equivalence in terms of their defining relations in the case that their point schemes are not elliptic curves. In the case that their point schemes are elliptic curves, we give conditions for isomorphism and graded Morita equivalence in terms of geometric data.
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キーワード | AS-regular algebras
geometric algebras
quadratic algebras
nodal cubic curves
elliptic curves
Hesse form
Sklyanin algebras
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備考 | Mathematics Subject Classification. 16W50, 16S37, 16D90, 16E65.
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発行日 | 2021-01
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出版物タイトル |
Mathematical Journal of Okayama University
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巻 | 63巻
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号 | 1号
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出版者 | Department of Mathematics, Faculty of Science, Okayama University
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開始ページ | 61
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終了ページ | 86
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ISSN | 0030-1566
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NCID | AA00723502
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資料タイプ |
学術雑誌論文
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言語 |
英語
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著作権者 | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
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論文のバージョン | publisher
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査読 |
有り
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Submission Path | mjou/vol63/iss1/4
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