On the Parameterization of Primitive Ideals in Affine Pi Algebras

In their fundamental studies of the finite dimensional representations of associative algebras, Artin and Procesi proved that the primitive ideals corresponding to irreducible n-dimensional representations (for fixed n, over an algebraically closed field) can be homeomorphically parameterized by a locally closed subset of the maximal spectrum of a suitably chosen affine commutative trace ring. In this paper we apply this theory to construct an open bijection from the whole primitive spectrum of an arbitary affine PI algebra (again over an algebraically closed field) onto a constructible subset of the maximal spectrum of a suitably chosen affine commutative trace ring.