Prime ideals invariant under winding automorphisms in quantum matrices
摘要
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.
引用
@article{arxiv.math/0110072,
title = {Prime ideals invariant under winding automorphisms in quantum matrices},
author = {K. R. Goodearl and T. H. Lenagan},
journal= {arXiv preprint arXiv:math/0110072},
year = {2007}
}
备注
36 pages. See also http://www.math.ucsb.edu/~goodearl/preprints.html/