 
Summary: Version 1.21, February, 1998. To appear in Trans. Amer. Math. Soc.
THE DIXMIERMOEGLIN EQUIVALENCE IN QUANTUM
COORDINATE RINGS AND QUANTIZED WEYL ALGEBRAS
K. R. Goodearl and E. S. Letzter
Abstract. We study prime and primitive ideals in a unified setting applicable to quanti
zations (at nonroots of unity) of n \Theta n matrices, of Weyl algebras, and of Euclidean and
symplectic space. The framework for this analysis is based upon certain iterated skew poly
nomial algebras A over infinite fields k of arbitrary characteristic. Our main result is the
verification, for A, of a characterization of primitivity established by Dixmier and Moeglin
for complex enveloping algebras. Namely, we show that a prime ideal P of A is primitive if
and only if the center of the Goldie quotient ring of A=P is algebraic over k, if and only if P
is a locally closed point  with respect to the Jacobson topology  in the prime spectrum of
A.
These equivalences are established with the aid of a suitable group H acting as automor
phisms of A. The prime spectrum of A is then partitioned into finitely many ``Hstrata'' (two
prime ideals lie in the same Hstratum if the intersections of their Horbits coincide), and we
show that a prime ideal P of A is primitive exactly when P is maximal within its Hstratum.
This approach relies on a theorem of MoeglinRentschler (recently extended to positive char
acteristic by Vonessen), which provides conditions under which H acts transitively on the set
of rational ideals within each Hstratum. In addition, we give detailed descriptions of the
