What question did this study set out to answer?

The aim is to connect exceptional Jordan algebra with associative Clifford algebra using the Fano plane.

July 26, 2026Open Access

From Exceptional Jordan Geometry to Clifford Algebra: An Immersive Bridge via the Fano Plane

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This research constructs a bridge between exceptional Jordan algebra and Clifford algebra, indicating new applications in quantum theories.

The aim is to connect exceptional Jordan algebra with associative Clifford algebra using the Fano plane.
Constructed a rigorous immersive bridge between exceptional Jordan algebra h_3(O)^C and a 14-dimensional Clifford algebra.
Utilized a hybrid representation of Spin(10) through its subgroup structure.
Validated findings with a reproducible numerical script.
Demonstrated the faithful realization of the stabilizer algebra of a rank-one idempotent in h_3(O)^C as a Clifford algebra subalgebra.
Confirmed injective differential and spectral invariants defined by the minimal polynomial m_X(x) = x^4 - 13x^2 + 30.
Established a direct algebraic link to potential applications in quantum field theory and tensor networks.

Massimiliano Blandino (2026) studied this question.

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This research constructs a bridge between exceptional Jordan algebra and Clifford algebra, indicating new applications in quantum theories.