Abstract
The main goal of the paper is to establish the existence of tensor product decompositions for those prime ideals P of the algebra [Formula: see text] of quantum n × 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 [Formula: see text] where A → A ⊗ A is the comultiplication, A+ and A- are suitable localized factor algebras of A, and P± is a prime ideal of A± invariant under winding automorphisms. Further, the algebras A±, which vary with P, can be chosen so that the correspondence (P+, P-) ↦ P is a bijection. The main theorem is applied, in a sequel to this paper, to completely determine the winding-invariant prime ideals in the generic quantum 3 × 3 matrix algebra.
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