A Complete Classification of 3-dimensional Quadratic AS-regular Algebras of Type EC
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Abstract Classification of AS-regular algebras is one of the main interests in noncommutative algebraic geometry. We say that a $3$ -dimensional quadratic AS-regular algebra is of Type EC if its point scheme is an elliptic curve in $\mathbb {P}^{2}$ . In this paper, we give a complete list of geometric pairs and a complete list of twisted superpotentials corresponding to such algebras. As an application, we show that there are only two exceptions up to isomorphism among all $3$ -dimensional quadratic AS-regular algebras that cannot be written as a twist of a Calabi–Yau AS-regular algebra by a graded algebra automorphism.
2012 ◽
Vol 55
(2)
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pp. 241-257
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2005 ◽
Vol 16
(06)
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pp. 595-607
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2016 ◽
Vol 72
(6)
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pp. 673-683
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