Lie Quandles, Leibniz Racks and Noether's First Theorem
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917458390024192 |
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| author | Elhamdadi, Mohamed Virgin, Bryce |
| author_facet | Elhamdadi, Mohamed Virgin, Bryce |
| contents | In [Self-distributive structures in physics. Internat. J. Theoret. Phys. 64 (2025), no. 3, Paper No. 73], Fritz was motivated by the structure of Hamiltonian/Heisenberg mechanics to define the notion of "Lie Quandle", which he argued are nonlinear generalizations of finite dimensional real Lie algebras. In this article, we will investigate a linear/nonlinear correspondence to which Fritz' is a special case, classify a class 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17043 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lie Quandles, Leibniz Racks and Noether's First Theorem Elhamdadi, Mohamed Virgin, Bryce Quantum Algebra Mathematical Physics Category Theory Geometric Topology Rings and Algebras In [Self-distributive structures in physics. Internat. J. Theoret. Phys. 64 (2025), no. 3, Paper No. 73], Fritz was motivated by the structure of Hamiltonian/Heisenberg mechanics to define the notion of "Lie Quandle", which he argued are nonlinear generalizations of finite dimensional real Lie algebras. In this article, we will investigate a linear/nonlinear correspondence to which Fritz' is a special case, classify a class 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. |
| title | Lie Quandles, Leibniz Racks and Noether's First Theorem |
| topic | Quantum Algebra Mathematical Physics Category Theory Geometric Topology Rings and Algebras |
| url | https://arxiv.org/abs/2604.17043 |