Destabilization
2015; Elsevier BV; Volume: 34; Issue: 1 Linguagem: Inglês
10.1016/j.exmath.2015.10.003
ISSN1878-0792
AutoresS. Kaliszewski, Tron Omland, John Quigg,
Tópico(s)Algebraic structures and combinatorial models
ResumoThis partly expository paper first supplies the details of a method of factoring a stable C ∗ -algebra A as B ⊗ K in a canonical way. Then it is shown that this method can be put into a categorical framework, much like the crossed-product dualities, and that stabilization gives rise to an equivalence between the nondegenerate category of C ∗ -algebras and a category of “ K -algebras”. We consider this equivalence as “inverting” the stabilization process, that is, a “destabilization”. Furthermore, the method of factoring stable C ∗ -algebras generalizes to Hilbert bimodules, and an analogous category equivalence between the associated enchilada categories is produced, giving a destabilization for C ∗ -correspondences. Finally, we make a connection with (double) crossed-product duality.
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