Family 294Operator algebrasLeanNot yet digested

Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness

Disproves Kaplansky's quasitrace conjecture by constructing a separable unital complex C

^{∗}

-algebra admitting normalized 2-quasitraces, all of which are nonadditive. As a consequence, two unital simple stably finite C

^{∗}

-algebras can have a properly infinite minimal tensor product, with one factor

C_r^*(\mathbb F_2)

Manuscripts in this family · 1

A counterexample to Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness

Sep 23, 2026·paper.pdfLean

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)

Full abstract

PDF on GitHub LaTeX source