Generalized integrable tops related to non-trivial solvable three dimensional Lie algebras

Jinrong Bao

doi:10.1016/j.geomphys.2025.105572

Generalized integrable tops related to non-trivial solvable three dimensional Lie algebras

Jinrong Bao

Department of Foundational Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The goal of this paper is to study and construct analogues of integrable tops related to three dimensional solvable Lie algebras in Bianchi types. We consider the semi-direct products of three dimensional solvable Lie algebras g and R ³ with respect to the natural representation. This representation and its dual are not isomorphic, so we discuss them separately. We find some integrable cases with explicit description.

Original language	English
Article number	105572
Journal	Journal of Geometry and Physics
Volume	216
DOIs	https://doi.org/10.1016/j.geomphys.2025.105572
Publication status	Published - Oct 2025

Keywords

Hamiltonian systems
Integrable tops
Lie algebras
Poisson-Lie brackets

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10.1016/j.geomphys.2025.105572

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title = "Generalized integrable tops related to non-trivial solvable three dimensional Lie algebras",

abstract = "The goal of this paper is to study and construct analogues of integrable tops related to three dimensional solvable Lie algebras in Bianchi types. We consider the semi-direct products of three dimensional solvable Lie algebras g and R 3 with respect to the natural representation. This representation and its dual are not isomorphic, so we discuss them separately. We find some integrable cases with explicit description.",

keywords = "Hamiltonian systems, Integrable tops, Lie algebras, Poisson-Lie brackets",

author = "Jinrong Bao",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier B.V.",

year = "2025",

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doi = "10.1016/j.geomphys.2025.105572",

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T1 - Generalized integrable tops related to non-trivial solvable three dimensional Lie algebras

AU - Bao, Jinrong

PY - 2025/10

Y1 - 2025/10

N2 - The goal of this paper is to study and construct analogues of integrable tops related to three dimensional solvable Lie algebras in Bianchi types. We consider the semi-direct products of three dimensional solvable Lie algebras g and R 3 with respect to the natural representation. This representation and its dual are not isomorphic, so we discuss them separately. We find some integrable cases with explicit description.

AB - The goal of this paper is to study and construct analogues of integrable tops related to three dimensional solvable Lie algebras in Bianchi types. We consider the semi-direct products of three dimensional solvable Lie algebras g and R 3 with respect to the natural representation. This representation and its dual are not isomorphic, so we discuss them separately. We find some integrable cases with explicit description.

KW - Hamiltonian systems

KW - Integrable tops

KW - Lie algebras

KW - Poisson-Lie brackets

UR - https://www.scopus.com/pages/publications/105009307994

U2 - 10.1016/j.geomphys.2025.105572

DO - 10.1016/j.geomphys.2025.105572

M3 - Article

SN - 0393-0440

VL - 216

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

M1 - 105572

ER -

Generalized integrable tops related to non-trivial solvable three dimensional Lie algebras

Abstract

Keywords

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