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The objective is to derive octonions and the Lie exceptional algebra G2 using Clifford algebra with positive definite signature.

Construction of Exceptional Lie Algebra G2 and Non-associative Algebras Using Clifford Algebra

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This article uncovers octonions and G2 using calibrations in Clifford algebra, suggesting novel algebraic structures.

The objective is to derive octonions and the Lie exceptional algebra G2 using Clifford algebra with positive definite signature.
Utilized Clifford algebra to derive octonions and G2.
Applied alternative calibration methods instead of the exterior algebra approach.
Examined the relationships between G2 and derived algebras through symmetry considerations.
Discovered a subalgebra related to Spin(7) that aids in classifying power-associative algebras.
Identified six new power-associative algebras linked to the symmetries of G2.
Presented a new construction of G2 without relying on the Lie bracket.

G. P. Wilmot (2026) studied this question.

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