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pith:NGWEPPST

pith:2026:NGWEPPSTITTP6WKOPFJ6MA5YAA

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Poisson Centralisers and Polynomial Superintegrability for Magnetic Geodesic Flows on Reductive Homogeneous Spaces

Guorui Ma, Ian Marquette, Junze Zhang, Kai Jiang, Yao-Zhong Zhang

Magnetic geodesic flows on reductive homogeneous spaces admit superintegrability through polynomial integrals from the Lie algebra and an invariant slice.

arxiv:2601.01369 v2 · 2026-01-04 · math-ph · math.MP

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Claims

C1strongest claim

Their common image generates a reduced Poisson algebra obtained from a fiber tensor product, and the natural multiplication map into a Poisson subalgebra of polynomial functions O(T^*M) subset C^infty(T^*M) is Poisson and injective. In a dense regular locus, the resulting projection chain realises a superintegrable system.

C2weakest assumption

The construction assumes the existence of an Ad(A)-invariant affine slice of m congruent to T_{eA}M and that the magnetic moment map P pulls back commuting polynomial integrals from g; this is stated as part of the setup for reductive homogeneous spaces but not derived in the abstract.

C3one line summary

Constructs two commuting families of polynomial first integrals for magnetic geodesic flows on reductive homogeneous spaces G/A, yielding a superintegrable system via a reduced Poisson algebra in a dense regular locus.

References

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[1] W. Miller Jr, S. Post, and P. Winternitz. Classical and quantum superintegrability with applications.J. Phys. A: Math. Theor., 46(42):423001, 97, 2013 2013

[2] N. Reshetikhin. Degenerately integrable systems.Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 433(Voprosy Kvantovo˘ ı Teorii Polya i Statistichesko˘ ı Fiziki. 23):224–245, 2015 2015

[3] J. Friˇ s, V. Mandrosov, Ya. A. Smorodinsky, M. Uhl´ ıˇ r, and P. Winternitz. On higher symmetries in quantum mechanics.Phys. Lett., 16:354–356, 1965 1965

[4] Action-angle variables and their generalizations.Trans 1968

[5] E. G. Kalnins, J. M. Kress, and W. Miller, Jr.Separation of variables and superintegrability. IOP Expanding Physics. IOP Publishing, Bristol, 2018. The symmetry of solvable systems 2018

Formal links

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Cited by

1 paper in Pith

Geometric construction of superintegrable Poisson projection chains via Poisson centralizers

Receipt and verification

First computed	2026-05-18T03:09:32.359585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69ac47be5344e6ff594e7953e603b8002a89c4c74f908903df2e836e15c1d850

Aliases

arxiv: 2601.01369 · arxiv_version: 2601.01369v2 · doi: 10.48550/arxiv.2601.01369 · pith_short_12: NGWEPPSTITTP · pith_short_16: NGWEPPSTITTP6WKO · pith_short_8: NGWEPPST

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Canonical record JSON

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    "abstract_canon_sha256": "ba8ec873b520742347a9d1ca0d5bbbb08c1f6367a9868f07cc3bb743c5a5d071",
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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-01-04T04:41:28Z",
    "title_canon_sha256": "1df3661dbc748778a4dcd9c6a5fb18d367a0ea2ee4fd7b3dfefc39df2c6385cb"
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