2001/10/05 by K. R. Goodearl, Goodearl, K. R., T. H. Lenagan +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Rings, Modules, and Algebras #math.QA #math.RA #msc:16W35 #msc:20G42
paper · pdf · doi:10.48550/arxiv.math/0110072
36 pages. See also http://www.math.ucsb.edu/~goodearl/preprints.html/
arxiv created 2001/10/05 · arxiv updated 2009/11/30
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.