Cocycle twists of 4-dimensional Sklyanin algebras

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• 作者：Andrew Davies ^{andrewpdavies@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：14A22 ; 16S35 ; 16S38 ; 16W22
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 July 2016
• 年：2016
• 卷：457
• 期：Complete
• 页码：323-360
• 全文大小：674 K

文摘

We study cocycle twists of a 4-dimensional Sklyanin algebra A and a factor ring B which is a twisted homogeneous coordinate ring. Twisting such algebras by the Klein four-group G  , we show that the twists A^G,μ$A^{G,\mu }$ and B^G,μ$B^{G,\mu }$ have very different geometric properties to their untwisted counterparts. For example, A^G,μ$A^{G,\mu }$ has only 20 point modules and infinitely many fat point modules of multiplicity 2. The ring B^G,μ$B^{G,\mu }$ falls under the purview of Artin and Stafford's classification of noncommutative curves, and we describe it using a sheaf of orders over an elliptic curve.