Ideal classes of three dimensional Artin–Schelter regular algebras

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• 作者：De Naeghel ; Koen ; Van den Bergh ; Michel
• 关键词：Weyl algebra ; Elliptic quantum planes ; Ideals ; Hilbert series
• 刊名：Journal of Algebra
• 出版年：2005
• 出版时间：January 1, 2005
• 年：2005
• 卷：283
• 期：1
• 页码：399-429
• 全文大小：264 K

文摘

We determine the possible Hilbert functions of graded rank one torsion free modules over three dimensional Artin–Schelter regular algebras. It turns out that, as in the commutative case, they are related to Castelnuovo functions. From this we obtain an intrinsic proof that the space of torsion free rank one modules on a non-commutative Formula Not Shown is connected. A different proof of this fact, based on deformation theoretic methods and the known commutative case has recently been given by Nevins and Stafford [Sklyanin algebras and Hilbert schemes of points, math.AG/0310045]. For the Weyl algebra it was proved by Wilson [Invent. Math. 133 (1) (1998) 1–41].