DIFFERENTIAL-OPERATORS AND FINITE-DIMENSIONAL ALGEBRAS

Let R be a Dedekind domain that is finitely generated over k, an algeb raically closed field of characteristic zero. Let M be a torsionfree m odule of rank one over a subalgebra of R with integral closure R. This paper investigates the structure of D(M), the ring of differential op erators on M. It is shown that D(M) has a unique minimal non-zero idea l, J(M), and that the factor, D(M)/J(M), is a finite-dimensional k-alg ebra. This factor is realised as the algebra of all endomorphisms of a n associated vector space that preserve certain subspaces. The main re sult is that given any finite-dimensional k-algebra A there exists suc h an M with A congruent to D(M)/J(M). (C) 1995 Academic Press, Inc.