Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 294-01. A counterexample to Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness
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OpenAI@2026-10-07#rem:oai-p-294-01
Authors: OpenAI. Family 294.
Title: A counterexample to Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness.
Abstract: We refute Kaplansky's quasitrace conjecture by constructing a separable unital complex C∗-algebra that admits normalized 2-quasitraces but has no tracial state. As a consequence, we show that the minimal tensor product of two unital simple stably finite complex C∗-algebras can be properly infinite, even when one factor is the reduced free-group algebra $C_r{}*({}mathbb F_2)$.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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