Cuntz-Krieger uniqueness theorem for crossed products by Hilbert bimodules

2010/10/03 by B. K. Kwaśniewski, Kwasniewski, B. K. · 3 citations
Mathematics · Physics and Astronomy · #46L05 #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1010.0446

openalex publication_date 2010/10/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

It is shown that a C*-algebra generated by any faithful covariant representation of a Hilbert bimodule X is canonically isomorphic to the crossed product associated to X provided that Rieffel's induced representation functor X-ind is topologically free. It is discussed how this result could be applied to universal C*-algebras generated by relations with a circle gauge action. In particular, it leads to generalizations of isomorphism theorems for various crossed products, and is shown to be equivalent to Cuntz-Krieger uniqueness theorem for finite graph C*-algebras (on that occasion an intriguing realization of Cuntz-Krieger algebras as crossed products by Exel's interactions is discovered).

Cited by

• C*-dynamical systems associated to Graph C*-Algebras
• Stacey crossed products associated to Exel systems
• Exel and Stacey crossed products, and Cuntz-Pimsner algebras

Related

• Exel's Crossed Product and Relative Cuntz-Pimsner Algebras
• The Toeplitz algebra of a Hilbert bimodule
• Cuntz-Pimsner C*-algebras and crossed products by Hilbert C*-bimodules
• Relative Cuntz-Pimsner Algebras, Partial Isometric Crossed Products and Reduction of Relations
• Cuntz-Krieger type uniqueness theorem for topological higher-rank graph C*-algebras