The 27-Dimensional Secret: Albert Algebras and the Geometry of Symmetry

Join us as we explore Albert algebras—the 27-dimensional Jordan algebras that bridge geometry, symmetry, and number theory. We'll see how their multiplication mirrors the 27 lines on a cubic surface, unpack their links to exceptional groups (G2, F4, E6), and recount the breakthrough discovery of a new isomorphism class over the integers via isotopes, all while outlining a two-pronged strategy of deep theory and brute-force computation guiding future discoveries.

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