2001/06/13 by Masaki Izumi, Izumi, Masaki
Mathematics · Physics and Astronomy · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.math/0106117
arxiv created 2001/06/13 · openalex publication_date 2001/06/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that if a conditional expectation from a simple C^*-algebra onto its C^*-subalgebra satisfies the Pimsner-Popa inequality, there exists a quasi-basis. As an application, we establish the Galois correspondence for outer actions of finite groups (and more generally finite dimensional Kac algebras) on simple C^*-algebras. We also introduce the notion of sectors for stable simple C^*-algebras and purely infinite simple C^*-algebras in the Cuntz standard form, and discuss several applications, including their relationship to K-theory.