Selfless Inclusions of C*-Algebras

2025/10/15 by Ben Hayes, Hayes, Ben, Srivatsav Kunnawalkam Elayavalli +5 · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #FOS: Mathematics #Fuzzy and Soft Set Theory #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2510.13398

openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

We introduce and study a natural notion of selflessness for inclusions of C*-probability spaces, which in particular implies that all intermediate C*-algebras are selfless in the sense of Robert. We identify natural sources of selfless inclusions in the realms of Z-stable and free product C*-algebras. As an application of this, we prove selflessness for a new family of C*-probability spaces outside the regime of free products and group C*-algebras. These include the reduced free unitary compact quantum groups.

Citations

• Proximality and selflessness for group C*-algebras
• The strong convergence phenomenon
• Strict comparison for twisted group C*-algebras
• Selfless reduced free product C^*-algebras
• Structural properties of reduced C^*-algebras associated with higher-rank lattices
• Negative resolution to the C^*-algebraic Tarski problem
• Selfless C*-algebras
• Amenability for unitary groups of simple monotracial C*-algebras
• Tensorially Absorbing Inclusions of C*-algebras
• A Dixmier type averaging property of automorphisms on a C^*-algebra
• Unitary Easy Quantum Groups: the free case and the group case
• Isomorphisms and Fusion Rules of Orthogonal Free Quantum Groups and their Complexifications
• The norm of polynomials in large random and deterministic matrices
• On the classification of nuclear C*-algebras

Cited by

• Selfless reduced free products and graph products of C^∗-algebras

Related

• Selfless C*-correspondences, operator valued C*-probability spaces and completely positive maps
• The Selfless Dichotomy
• Selfless reduced free product C^*-algebras
• Proximality and selflessness for group C*-algebras
• Selfless C*-algebras