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A new Lie algebra expansion method: Galilei expansions to Poincare and Newton-Hooke

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Francisco J. Herranz, Mariano Santander

Mathematical Physics · Submitted 2 Sep 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This new improved and geometrical procedure is applied to expanding the (3+1)-dimensional Galilei algebra and leads to its physically meaningful `expanded' neighbours.

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arXiv IDmath-ph/9909005 (version 2)
Pith IDDNE6SLHY, Pith's permanent record of this paper and its review
CitationFrancisco J. Herranz, Mariano Santander. "A new Lie algebra expansion method: Galilei expansions to Poincare and Newton-Hooke." arXiv:math-ph/9909005 (1999). https://pith.science/paper/DNE6SLHY
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,466 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.19 · compares with prior results 0.78 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; .

We modify a Lie algebra expansion method recently introduced for the (2+1)-dimensional kinematical algebras so as to work for higher dimensions. This new improved and geometrical procedure is applied to expanding the (3+1)-dimensional Galilei algebra and leads to its physically meaningful `expanded' neighbours. One expansion gives rise to the Poincare algebra, introducing a curvature $-1/c^2$ in the flat Galilean space of worldlines, while keeping a flat spacetime which changes from absolute to relative time in the process. This formally reverses, at a Lie algebra level, the well known non-relativistic contraction $c\to \infty$ that goes from the Poincare group to the Galilei one; this expansion is done in an explicit constructive way. The other possible expansion leads to the Newton-Hooke algebras, endowing with a non-zero spacetime curvature $\pm 1/\tau^2$ the spacetime, while keeping a flat space of worldlines.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We modify a Lie algebra expansion method recently introduced for the (2+1)-dimensional kinematical algebras so as to work for higher dimensions. contribution 0.94 0.91 0.09 asserted 1.00
s1 This new improved and geometrical procedure is applied to expanding the (3+1)-dimensional Galilei algebra and leads to its physically meaningful `expanded' neighbours. contribution 0.73 0.94 0.27 asserted 1.00
s2 One expansion gives rise to the Poincare algebra, introducing a curvature $-1/c^2$ in the flat Galilean space of worldlines, while keeping a flat spacetime which changes from absolute to relative time in the process. result 0.90 0.88 0.29 asserted 1.00
s3 This formally reverses, at a Lie algebra level, the well known non-relativistic contraction $c\to \infty$ that goes from the Poincare group to the Galilei one; this expansion is done in an explicit constructive way. interpretation 0.93 0.86 0.17 asserted 1.00
s4 The other possible expansion leads to the Newton-Hooke algebras, endowing with a non-zero spacetime curvature $\pm 1/\tau^2$ the spacetime, while keeping a flat space of worldlines. result 0.98 0.88 0.16 asserted 0.87

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

We modify a Lie algebra expansion method recently introduced for the (2+1)-dimensional kinematical algebras so as to work for higher dimensions. This new improved and geometrical procedure is applied to expanding the (3+1)-dimensional Galilei algebra and leads to its physically meaningful `expanded' neighbours. One expansion gives rise to the Poincare algebra, introducing a curvature $-1/c^2$ in the flat Galilean space of worldlines, while keeping a flat spacetime which changes from absolute to relative time in the process. This formally reverses, at a Lie algebra level, the well known non-relativistic contraction $c\to \infty$ that goes from the Poincare group to the Galilei one; this expansion is done in an explicit constructive way. The other possible expansion leads to the Newton-Hooke algebras, endowing with a non-zero spacetime curvature $\pm 1/\tau^2$ the spacetime, while keeping a flat space of worldlines.

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