Classifying orders in the Sklyanin algebra

D. Rogalski, Susan J. Sierra, J. T. Stafford

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

Let S denote the 3-dimensional Sklyanin algebra over an algebraically closed field k and assume that S is not a nite module over its centre. (This algebra orresponds to a generic noncommutative P2.) Let A = ⊕i≥0Ai 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-eective) 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.
Original languageEnglish
Pages (from-to)2055-2119
JournalAlgebra & Number Theory
Volume9
Issue number9
DOIs
Publication statusPublished - 4 Nov 2015

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