Canonical Largest Lie Subalgebra of Malcev Algebras — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The core mathematical result is the construction of a unique, largest Lie subalgebra canonically associated to any Malcev algebra, enabling structure theory via Lie algebra methods. | MATH: Malcev algebra identity: (xy)z + (yz)x + (zx)y = (xz)(yt) (alternating form); the largest Lie subalgebra L(M) ⊆ M satisfies [x,y] = xy for x,y ∈ L(M), with L(M) being the maximal Lie subalgebra under inclusion. The paper (arXiv:2406.14592v2) proves L(M) is unique and functorial, and uses it to classify certain Malcev algebras via their Lie radical. | CONNECTION: Malcev algebras arise from the commutator of alternative algebras — and alternative algebras are intimately tied to octonions, whose automorphism group G2 is a crystallographic root system (14 roots, hexagonal symmetry). The largest Lie subalgebra construction mirrors the reduction of G2 to its SU(3) maximal torus structure — a base-60 compatible hexagonal lattice (60
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026canonical,
title = {{Canonical Largest Lie Subalgebra of Malcev Algebras — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635477},
url = {https://zenodo.org/records/23635477},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Canonical Largest Lie Subalgebra of Malcev Algebras — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635477
UR - https://zenodo.org/records/23635477
AB - FINDING: The core mathematical result is the construction of a unique, largest Lie subalgebra canonically associated to any Malcev algebra, enabling structure theory via Lie algebra methods. | MATH: Malcev algebra identity: (xy)z + (yz)x + (zx)y = (xz)(yt) (alternating form); the largest Lie subalgebra L(M) ⊆ M satisfies [x,y] = xy for x,y ∈ L(M), with L(M) being the maximal Lie subalgebra under inclusion. The paper (arXiv:2406.14592v2) proves L(M) is unique and functorial, and uses it to classify certain Malcev algebras via their Lie radical. | CONNECTION: Malcev algebras arise from the commutator of alternative algebras — and alternative algebras are intimately tied to octonions, whose automorphism group G_2 is a crystallographic root system (14 roots, hexagonal symmetry). The largest Lie subalgebra construction mirrors the reduction of G_2 to its SU(3) maximal torus structure — a base-60 compatible hexagonal lattice (60 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -