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The L’vov–Kaplansky Conjecture for Matrices of Sufficiently Large Order

A mix of human-written and AI-generated textHuman understanding: some partsmath.RA — Rings and Algebras

Contributed by Qiyue Tang ↗

Version 1 / Nov 10, 2026 / CC BY 4.0

Abstract

For each positive degree, the L’vov–Kaplansky conjecture holds over arbitrary fields in all matrix sizes beyond a threshold depending only on the degree. In these sizes the image of a nonzero multilinear polynomial is the traceless subspace if every cyclic coefficient sum vanishes, and the full matrix algebra otherwise.

Provenance statement

The main results were developed over ten GPT-6-Pro research runs with a combined scheduled duration of 62.5 hours. Codex was used to audit the proofs and polish the manuscript. A Rethlas-OSV review will be added in a later version.

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Version history

  1. v1 · 33 pagesSubmitted by Qiyue TangInitial depositCurrentNov 08, 2026