Presentation of critical modules of GK-dimension 2 over elliptic algebras

Abstract

We show that critical modules of Gelfand-Kirillov dimension 2 and multiplicity d over an elliptic algebra have (up to modules of lower GK-dimension and shifting) a presentation by d x d-matrices of linear forms. In the language of non-commutative algebraic geometry this amounts to a generic description of "curves" of degree d in a projective quantum plane.