analysis / Operator algebras: free probability, free entropy

Voiculescu's question: is free entropy dimension an invariant of the generated von Neumann algebra?

Claims a negative answer for δ\delta, δ0\delta_0, δ∗\delta^* and δ⋆\delta^\star: each takes every integer value n≥2n\ge2 on finite self-adjoint generating tuples of the single factor L(F2)L(\mathbb F_2), obtained by transporting semicircular and group-algebra tuples through the new isomorphisms. It does not compute free entropy dimension for other algebras or address the microstates-free equality questions.

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analysisSep 23, 2026Significance 38/100Registry: unreviewed

Voiculescu's question: is free entropy dimension an invariant of the generated von Neumann algebra?

Prior state unknown→disproved

Claims a negative answer for δ\delta, δ0\delta_0, δ∗\delta^* and δ⋆\delta^\star: each takes every integer value n≥2n\ge2 on finite self-adjoint generating tuples of the single factor L(F2)L(\mathbb F_2), obtained by transporting semicircular and group-algebra tuples through the new isomorphisms. It does not compute free entropy dimension for other algebras or address the microstates-free equality questions.

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Claims a negative answer for δ\delta, δ0\delta_0, δ∗\delta^* and δ⋆\delta^\star: each takes every integer value n≥2n\ge2 on finite self-adjoint generating tuples of the single factor L(F2)L(\mathbb F_2), obtained by transporting semicircular and group-algebra tuples through the new isomorphisms. It does not compute free entropy dimension for other algebras or address the microstates-free equality questions.

Claims a negative answer for δ\delta, δ0\delta_0, δ∗\delta^* and δ⋆\delta^\star: each takes every integer value n≥2n\ge2 on finite self-adjoint generating tuples of the single factor L(F2)L(\mathbb F_2), obtained by transporting semicircular and group-algebra tuples through the new isomorphisms. It does not compute free entropy dimension for other algebras or address the microstates-free equality questions.

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Voiculescu's question: is free entropy dimension an invariant of the generated von Neumann algebra? — Mathematical Frontier Network