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• W3100499751 startingPage "2055" @default.
• W3100499751 abstract "One of the major open problems in noncommutative algebraic geometry is the classification of noncommutative surfaces, and this paper resolves a significant case of this problem. Specifically, let S denote the 3-dimensional Sklyanin algebra over an algebraically closed field k and assume that S is not a finite module over its centre. (This algebra corresponds to a generic noncommutative P^2.) Let A be any connected graded k-algebra that is contained in and has the same quotient ring as a Veronese ring S^(3n). Then we give a reasonably complete description of the structure of A. This is most satisfactory when A is a maximal order, in which case we prove, subject to a minor technical condition, that A is a noncommutative blowup of S^(3n) at a (possibly non-effective) divisor on the associated elliptic curve E. It follows that A has surprisingly pleasant properties; for example it is automatically noetherian, indeed strongly noetherian, and has a dualizing complex." @default.
• W3100499751 created "2020-11-23" @default.
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• W3100499751 date "2015-11-04" @default.
• W3100499751 modified "2023-10-16" @default.
• W3100499751 title "Classifying orders in the Sklyanin algebra" @default.
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• W3100499751 doi "https://doi.org/10.2140/ant.2015.9.2055" @default.
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