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arXiv · 1512.05717

Cocycle twists of 4-dimensional Sklyanin algebras

Andrew Davies
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Abstract

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 $A^{G,μ}$ and $B^{G,μ}$ have very different geometric properties to their untwisted counterparts. For example, $A^{G,μ}$ has only 20 point modules and infinitely many fat point modules of multiplicity 2. The ring $B^{G,μ}$ 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.

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Andrew Davies. 2016-01-14. Cocycle twists of 4-dimensional Sklyanin algebras. https://arxiv.org/abs/1512.05717

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