A Cubic Heisenberg Centralizer and Non-flat Diamond Argument-Shift Maps
Manuscript 24 October 2026 · Online 24 October 2026
Abstract
We compute two small examples separating maximality, maximal transcendence degree and flatness in symmetric Poisson algebras. For the four-dimensional diamond Lie algebra we classify the regular argument shifts whose natural morphisms are flat. The shift at x* is not flat despite satisfying the full codimension-three and invariant-degree hypotheses of the Panyushev-Yakimova maximality theorem. The underlying example and its shift algebra are due to Ooms. For the five-dimensional Heisenberg algebra, the homogeneous cubic F=2z^2t+zp^2-xq^2 has Poisson centralizer k[z,F], a maximal commutative polynomial algebra of transcendence degree two, below the maximal value three. An elementary weighted-degree obstruction for the Airy derivation proves the centralizer formula in all degrees. Ooms's earlier unrestricted negative answer to the maximality/dimension question is explicitly credited. This is an unrefereed manuscript, with AI assistance disclosed in the text and no absolute priority claim. Source dataset record: OWR-1538-001 (ulamai/UnsolvedMath v1.6.0). The manuscript discloses OpenAI Codex assistance.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Explicit counterexamples
- Categories
- math.RA · math.AG · math.RT
- Manuscript
- 24 October 2026
- Online release
- 24 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “A Cubic Heisenberg Centralizer and Non-flat Diamond Argument-Shift Maps,” EulerSolve Research Papers, OWR-1538-001, 2026. https://doi.org/10.5281/zenodo.23621691.
BibTeX
@misc{ferudun2026poissoncentralizer,
author = {Ferudun, Alper},
title = {A Cubic Heisenberg Centralizer and Non-flat Diamond Argument-Shift Maps},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/owr-1538-001/},
doi = {10.5281/zenodo.23621691},
note = {OWR-1538-001; unrefereed preprint}
}