Abstract
Let denote the 3-dimensional Sklyanin algebra over an algebraically closed field and assume that is not a finite module over its centre. (This algebra corresponds to a generic noncommutative .) Let be any connected graded -algebra that is contained in and has the same quotient ring as a Veronese ring . Then we give a reasonably complete description of the structure of . This is most satisfactory when is a maximal order, in which case we prove, subject to a minor technical condition, that is a noncommutative blowup of at a (possibly noneffective) divisor on the associated elliptic curve . It follows that has surprisingly pleasant properties; for example, it is automatically noetherian, indeed strongly noetherian, and has a dualising complex.
Citation
Daniel Rogalski. Susan Sierra. J. Stafford. "Classifying orders in the Sklyanin algebra." Algebra Number Theory 9 (9) 2055 - 2119, 2015. https://doi.org/10.2140/ant.2015.9.2055
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