 
Summary: PRIME IDEALS INVARIANT UNDER WINDING
AUTOMORPHISMS IN QUANTUM MATRICES
K. R. Goodearl and T. H. Lenagan
Abstract. The main goal of the paper is to establish the existence of tensor product decom
positions for those prime ideals P of the algebra A = Oq (Mn (k)) of quantum n \Theta n matrices
which are invariant under winding automorphisms of A, in the generic case (q not a root of
unity). More specifically, every such P is the kernel of a map of the form
A \Gamma!
A\Omega A \Gamma! A
+\Omega A \Gamma \Gamma! (A + =P +
)\Omega (A \Gamma =P \Gamma )
where A !
A\Omega A is the comultiplication, A + and A \Gamma are suitable localized factor algebras
of A, and P \Sigma is a prime ideal of A \Sigma invariant under winding automorphisms. Further, the
algebras A \Sigma , which vary with P , can be chosen so that the correspondence (P + ; P \Gamma ) 7! P is
a bijection. The main theorem is applied, in a sequel to this paper, to completely determine
the windinginvariant prime ideals in the generic quantum 3 \Theta 3 matrix algebra.
Introduction
This paper represents part of an ongoing project to determine the prime and primitive
spectra of the generic quantized coordinate ring of n \Theta n matrices, O q (M n (k)). Here k is
