A major current goal of noncommutative geometry is the classification of noncommutative projective surfaces. The generic case is to understand algebras birational to the Sklyanin algebra. In this thesis we complete a considerable component of this problem. Let S denote the 3dimensional Sklyanin algebra over an algebraically closed field, and assume that S is not a finite module over its centre. In earlier work Rogalski, Sierra and Stafford classified the maximal orders inside the 3Veronese of S. We complete and extend their work and classify all maximal orders inside S. As in Rogalski, Sierra and Stafford's work, these can be viewed as blowups at (possibly noneffective) divisors. A consequence of this classification is that maximal orders are automatically noetherian among other desirable properties. This work both relies upon, and lends back to, the work of Rogalski, Sierra and Stafford. In particular, we also provide a converse for their classification of maximal orders in the higher Veronese subrings of S.
Date of Award  1 Aug 2019 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Stafford (Supervisor) & Yuri Bazlov (Supervisor) 

Maximal Orders in the Sklyanin Algebra
Bush Hipwood, L. (Author). 1 Aug 2019
Student thesis: Phd