Prime ideals invariant under winding automorphisms in quantum matrices

الأصل · EN

The main goal of the paper is to establish the existence of tensor product decompositions for those prime ideals P of the generic algebra A of quantum n by n matrices which are invariant under winding automorphisms of A. More specifically, every such P is the kernel of a map from A to (A+/P+) tensor (A-/P-) obtained by composing comultiplication, localization, and quotient maps, where A+ and A- are special localized quotients of A while P+ and P- are prime ideals invariant under winding automorphisms. Further, the algebras A+ and A-, which vary with P, can be chosen so that the correspondence sending (P+,P-) to 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 by 3 matrix algebra.