No Evidence for G2 Subalgebra Dimension Ratio in 7-Dimensional Simple Malcev Algebras — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search returned no result on a "7-dimensional simple Malcev algebra G2 Lie subalgebra dimension ratio." The retrieved material is generic Lie-algebra pedagogy (sl(2) subalgebras, sl_2(C)-modules, SU(2)) plus one structural paper on the Lie algebra associated to a Malcev algebra. No 7-dimensional simple Malcev algebra, no G2 subalgebra, and no dimension ratio appears in the evidence.
MATH: - Malcev algebra defining identity (from the arXiv paper): (xy)(xz) = ((xy)z)x + ((yz)x)x + ((zx)x)y — a Malcev algebra is a non-associative algebra satisfying this, generalizing Lie algebras (which additionally satisfy anticommutativity + Jacobi). - Standard fact (not in the retrieved text, but the only rigorous anchor for the query): the only simple finite-dimensional Malcev algebra that is not a Lie algebra is the 7-dimensional one, which is the traceless part of the Cayley (octonion) algebra, sl(2,𝕆) ≅ 𝕆₀, with multiplication [x,y] = xy − yx. - G2 = Aut(𝕆) = Der(𝕆), dim G2 = 14. Its
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026evidence,
title = {{No Evidence for G2 Subalgebra Dimension Ratio in 7-Dimensional Simple Malcev Algebras — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658592},
url = {https://zenodo.org/records/23658592},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - No Evidence for G2 Subalgebra Dimension Ratio in 7-Dimensional Simple Malcev Algebras — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658592
UR - https://zenodo.org/records/23658592
AB - FINDING: The search returned no result on a "7-dimensional simple Malcev algebra G2 Lie subalgebra dimension ratio." The retrieved material is generic Lie-algebra pedagogy (sl(2) subalgebras, sl_2(C)-modules, SU(2)) plus one structural paper on the Lie algebra associated to a Malcev algebra. No 7-dimensional simple Malcev algebra, no G2 subalgebra, and no dimension ratio appears in the evidence. MATH: - Malcev algebra defining identity (from the arXiv paper): (xy)(xz) = ((xy)z)x + ((yz)x)x + ((zx)x)y — a Malcev algebra is a non-associative algebra satisfying this, generalizing Lie algebras (which additionally satisfy anticommutativity + Jacobi). - Standard fact (not in the retrieved text, but the only rigorous anchor for the query): the only simple finite-dimensional Malcev algebra that is not a Lie algebra is the 7-dimensional one, which is the traceless part of the Cayley (octonion) algebra, sl(2,𝕆) ≅ 𝕆₀, with multiplication [x,y] = xy − yx. - G2 = Aut(𝕆) = Der(𝕆), dim G2 = 14. Its Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -