OpenAI research collection · 1 manuscript · Source checked 2026-10-19
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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.
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MANUSCRIPT 01
The trace cone classifies Razak–Jacelon stabilizations
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…
Full source abstract
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.
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