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May 25, 2026Open Access

Uniqueness of E7 Among Simple Lie Algebras Under Gaussian Prime Norm Filtration

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Authors

RKRobert A. Kenney

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Overview

Randomized trial shows uniqueness of E7 in simple Lie algebras, indicating important mathematical properties.

Key Points

  • The research aims to demonstrate that E7 is the only simple Lie algebra satisfying specific primality conditions.
  • Exhaustive enumeration of simple Lie algebras including classical families and exceptional algebras.
  • Application of a three-layer sieve: Fermat splitting, congruence conditions, and cascade generation rules.
  • Verification of the uniqueness of the sum 137 = 133 + 4 for E7's dimensionality and max_mark.
  • E7 is uniquely identified as the simple Lie algebra where dim(g) + max_mark(Ĝ) meets the prime and Gaussian prime criteria.
  • Max_mark is confirmed as 4, supporting the uniqueness condition.
  • The dimensional decompositions for E7 align with the established theoretical framework.

Cite This Study

Robert A. Kenney (2026) studied this question.

synapsesocial.com/papers/6a13e8030e02ee3982d32b26https://doi.org/10.5281/zenodo.20360309
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