Destabilization

2015/03/03 by S. Kaliszewski, Kaliszewski, S., Tron Omland +3
Mathematics · #46L05 (Primary) #46L08 #46M15 #Advanced Operator Algebra Research #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #Secondary 46L06

paper · pdf · doi:10.48550/arxiv.1503.01151

openalex publication_date 2015/03/03 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28

Abstract

This 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.

Related

• Forking and stability in the representations of a C*-algebra
• Rational K-Stability of Continuous C(X)-Algebras
• C*-Algebraic Factorization Homology and Realization of Cyclic Representations
• Irreducible Induced Representations of Fell Bundle C*-Algebras
• Homotopy theory of C*-algebras