Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 22 (2026), 096, 15 pages      arXiv:2604.17043      https://doi.org/10.3842/SIGMA.2026.096

Lie Quandles, Leibniz Racks and Noether's First Theorem

Mohamed Elhamdadi and Bryce Virgin
Department of Mathematics and Statistics, University of South Florida, Tampa, Florida, USA

Received May 05, 2026, in final form September 21, 2026; Published online October 08, 2026

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.

Key words: Lie quandles; Leibniz algebras; Leibniz racks; Noether's first theorem.

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