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This work aims to establish the complete mathematical structure of the Lie algebra su(26) and validate it through computational modules and checks.

July 5, 2026Open Access

Complete Lie Algebra of SU(26) — Mathematical Foundation: 31 Computational Modules, 72 Cross-Checks

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This work aims to establish the complete mathematical structure of the Lie algebra su(26) and validate it through computational modules and checks.
Developed 31 computational modules for various aspects of the Lie algebra, including representations and decompositions.
Verified results through 72 cross-checks and produced a comprehensive catalog of irreducible representations.
Utilized software tools in Python for calculations and methodology.
Established a complete structure of su(26) with 2926 irreducible representations and verified tensor product decompositions.
Provided a modular S-matrix for SU(26)₃ and confirmed Gelfand-Tsetlin branching results for full catalog.
Achieved validation for all computational modules and cross-checks, ensuring robustness of findings.

Implication

Randomized trial reveals the mathematical structure of SU(26) Lie algebra, indicating robust verification of modules and representations.

Abstract

Complete mathematical structure of the Lie algebra su(26) of type A_25. 31 computational modules covering:- Root system A_25 and Weyl group S_26- Catalog of 2926 irreducible representations with Casimir operators- 7 tensor product decompositions (all verified)- Littlewood-Richardson decompositions (Ad⊗Ad, Λ²⊗Λ²)- Gelfand-Tsetlin branching (verified for full catalog)- Modular S-matrix for SU(26)₃ via logarithmic method- Affine Lie algebra ŝu(26)₁- Quantum group U_q(su(26))- 72 cross-checks (all passed) Companion physics paper: Σ-Ω⁴: A Complete Theory of Everything from SU(26) Gauge SymmetryDOI: 10.5281/zenodo.21143771 Software: Python 3.8+, NumPy. License: CC BY-NC-ND 4.0 International. Zenodo DOI: 10.5281/zenodo.21179695

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Cite This Study

Sergey Viktorovich Matershov (2026) studied this question.

synapsesocial.com/papers/6a49f70df5d1d45b2880114c https://doi.org/10.5281/zenodo.21179695

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Implication

Randomized trial reveals the mathematical structure of SU(26) Lie algebra, indicating robust verification of modules and representations.

Complete Lie Algebra of SU(26) — Mathematical Foundation: 31 Computational Modules, 72 Cross-Checks

Key Points

Implication

Abstract

Discussion

Cite This Study

Complete Lie Algebra of SU(26) — Mathematical Foundation: 31 Computational Modules, 72 Cross-Checks

Key Points

Implication

Abstract

Discussion

Cite This Study

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