Abstract
Let S denote the 3dimensional 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 P^{2}.) Let A = ⊕_{i≥0}Ai be any connected graded kalgebra 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 noneective) 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 language  English 

Pages (fromto)  20552119 
Journal  Algebra & Number Theory 
Volume  9 
Issue number  9 
DOIs  
Publication status  Published  4 Nov 2015 
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Sue Sierra
 School of Mathematics  Personal Chair of Noncommutative Algebra
Person: Academic: Research Active