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.
|Journal||Algebra & Number Theory|
|Publication status||Published - 4 Nov 2015|
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- School of Mathematics - Personal Chair of Noncommutative Algebra
Person: Academic: Research Active