Family 301Operator algebrasLeanNot yet digested
Trace cones and Razak–Jacelon stabilization
Classifies separable nuclear complex C-algebras after tensoring with the Razak–Jacelon algebra and the compact operators, using their full topological cones of extended lower-semicontinuous tracial weights. This answers Robert’s trace-cone question, including algebras with arbitrary ideal structure and both finite and infinite subquotients.
Manuscripts in this family · 1
The trace cone classifies Razak–Jacelon stabilizations
Sep 25, 2026·The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026.pdfLean
We prove that the canonical topological cone of all extended lower-semicontinuous tracial weights determines a separable nuclear C-algebra after tensoring with the Razak–Jacelon algebra and the compact operators, answering Robert's trace-cone classification question positively. The isomorphism realizes the prescribed cone map, with arbitrary ideal structure and without a density assumption on the finite domains of the weights.