Inner coactions, Fell bundles, and abstract uniqueness theorems

2011/08/25 by S. Kaliszewski, Kaliszewski, S., Nadia S. Larsen +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1108.5030

openalex publication_date 2011/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove gauge-invariant uniqueness theorems with respect to maximal and normal coactions for C^*-algebras associated to product systems of C^*-correspondences. Our techniques of proof are developed in the abstract context of Fell bundles. We employ inner coactions to prove an essential-inner uniqueness theorem for Fell bundles. As application, we characterise injectivity of homomorphisms on Nica's Toeplitz algebra \Tt(G, P) of a quasi-lattice ordered group (G, P) in the presence of a finite non-trivial set of lower bounds for all non-trivial elements in P.

Citations

• C*-algebras associated to product systems of Hilbert bimodules

Related

• Gauge-invariant uniqueness theorems for P-graphs
• Cuntz-Nica-Pimsner algebras of product systems over groupoids
• Coactions and Fell bundles
• Coactions of compact groups on M_n
• Fell bundles over quasi-lattice ordered groups and C^*-algebras of compactly aligned product systems