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This work aims to develop a matrix-theoretic framework for understanding octonionic triality within the context of the Lie algebra g2 and its applications in geometry.

June 27, 2026AxiomsOpen Access

Octonionic Triality, the Matrix Structure of g2, and Principal Bundle Moduli Spaces

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ÁAÁlvaro Antón‐SanchoUniversidad de Valladolid

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Randomized trial explores octonionic triality and its geometric applications in principal bundles, suggesting new insights on moduli spaces.

Key Points

This work aims to develop a matrix-theoretic framework for understanding octonionic triality within the context of the Lie algebra g2 and its applications in geometry.
Developed a matrix-theoretic framework for the embedding of g2 in so(8).
Reformulated the condition for D^∈so(7) as a homogeneous linear system.
Globalized the map Ψ to characterize G2-reductible loci in moduli spaces.
RankΨ was proven to equal 7, indicating a significant structural property of the Lie algebra.
Six nonzero components and squared norm 12 were computed for the triality generator images.
Identified M(G2) as a connected component in M(Spin(8)), detailing tangent and normal space descriptions.

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Álvaro Antón‐Sancho (2026) studied this question.

synapsesocial.com/papers/6a3f6817aea7db3c1953f475 https://doi.org/10.3390/axioms15070475

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Implication

Randomized trial explores octonionic triality and its geometric applications in principal bundles, suggesting new insights on moduli spaces.

Octonionic Triality, the Matrix Structure of g2, and Principal Bundle Moduli Spaces

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Implication

Key Points

Cite This Study

Octonionic Triality, the Matrix Structure of g2, and Principal Bundle Moduli Spaces

Discussion

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Implication

Key Points

Cite This Study

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