## Abstract

We provide a Lie algebra expansion procedure to construct three-dimensional higher-order Schrödinger algebras which relies on a particular subalgebra of the four-dimensional relativistic conformal algebra. In particular, we reproduce the extended Schrödinger algebra and provide a new higher-order Schrödinger algebra. The structure of this new algebra leads to a discussion on the uniqueness of the higher-order non-relativistic algebras. Especially, we show that the recent d-dimensional symmetry algebra of an action principle for Newtonian gravity is not uniquely defined but can accommodate three discrete parameters. For a particular choice of these parameters, the Bargmann algebra becomes a subalgebra of that extended algebra which allows one to introduce a mass current in a Bargmann-invariant sense to the extended theory.

Original language | English |
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Article number | 67 |

Journal | Journal of High Energy Physics |

Volume | 2020 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Apr 2020 |

### Bibliographical note

Publisher Copyright:© 2020, The Author(s).

### Funding

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

Funders | Funder number |
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Creative Commons Attribution License |

## Keywords

- Chern-Simons Theories
- Classical Theories of Gravity
- Space-Time Symmetries