Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-Dimensional Higher-Order Schr\"odinger Algebras and Lie Algebra
  Expansions   We provide a Lie algebra expansion procedure to construct three-dimensional
higher-order Schr\"odinger algebras which relies on a particular subalgebra of
the four-dimensional relativistic conformal algebra. In particular, we
reproduce the extended Schr\"odinger algebra and provide a new higher-order
Schr\"odinger 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.

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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph