Seminar

An "elliptic Weyl algebra" is obtained by localising a (generic) Sklyanin algebra at the central element g.  It is a hereditary domain of GK-dimension 2 that has the surprising and beautiful property that all of its subalgebras are finitely generated and noetherian.  We present the classification of maximal orders in elliptic Weyl algebras and give some consequences, focusing on the ideal structure.  We show that any order in an elliptic Weyl algebra has DCC on ideals, and deduce that any graded order in (the 3rd Veronese of) a Sklyanin algebra must be noetherian.  This is joint work with Dan Rogalski and Toby Stafford.