Prime ideals invariant under winding automorphisms in quantum matrices

Details Prime ideals invariant under winding automorphisms in quantum matrices Prime ideals invariant under winding automorphisms in quantum matrices

2001-10-05

arxiv.org/abs/math/0110072v1

Mathematics

Quantum Algebra

36 pages. See also http://www.math.ucsb.edu/~goodearl/preprints.html/

Scientific paper

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.

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