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Peer-reviewedCC BY-SA 4.0Symmetry, Integrability and Geometry: Methods and Applications

Lie Quandles, Leibniz Racks and Noether's First Theorem

  • Mohamed Elhamdadi1
  • Bryce Virgin1
  1. 1University of South Florida, USA
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Abstract

In [Internat. J. Theoret. Phys. 64 (2025), 73, 10 pages], Fritz was motivated by the structure of Hamiltonian/Heisenberg mechanics to define the notion of ''Lie quandle'', which he argued is a nonlinear generalization of finite-dimensional real Lie algebras. In this article, we will investigate a linear/nonlinear correspondence to which Fritz's is a special case, classify a family of generalizations of these objects, as well as describe some results in the direction of a nonlinear analogue of Noether's first theorem first described by Fritz.

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Cite

BibTeXRIS
BibTeX
@article{elhamdadi2026quandles,
  title = {{Lie Quandles, Leibniz Racks and Noether's First Theorem}},
  author = {Mohamed Elhamdadi and Bryce Virgin},
  journal = {Symmetry, Integrability and Geometry: Methods and Applications},
  year = {2026},
  month = oct,
  doi = {10.3842/sigma.2026.096},
  url = {https://sigma-journal.com/2026/096/},
  note = {CC BY-SA 4.0},
}
RIS
TY  - JOUR
TI  - Lie Quandles, Leibniz Racks and Noether's First Theorem
AU  - Mohamed Elhamdadi
AU  - Bryce Virgin
PY  - 2026
DA  - 2026/10/08
JO  - Symmetry, Integrability and Geometry: Methods and Applications
DO  - 10.3842/sigma.2026.096
UR  - https://sigma-journal.com/2026/096/
AB  - In [Internat. J. Theoret. Phys. 64 (2025), 73, 10 pages], Fritz was motivated by the structure of Hamiltonian/Heisenberg mechanics to define the notion of ''Lie quandle'', which he argued is a nonlinear generalization of finite-dimensional real Lie algebras. In this article, we will investigate a linear/nonlinear correspondence to which Fritz's is a special case, classify a family of generalizations of these objects, as well as describe some results in the direction of a nonlinear analogue of Noether's first theorem first described by Fritz.
SN  - 1815-0659
ER  -