Rational invariants of three frames in the split Albert algebra: a Lean formalization
Let J be the split Albert algebra over a field k of characteristic zero, the 27-dimensional Jordan algebra of 3 by 3 Hermitian matrices over the split octonions, with trace tr. A frame is an ordered triple of trace-one idempotents summing to 1. Three frames E, F, K carry 54 natural invariants under the group G of all unital k-linear bijections of J preserving its Jordan product: the pair traces tr(eᵢ∘fⱼ), tr(fⱼ∘kₗ), tr(kₗ∘eᵢ) and the triple traces tr(eᵢ∘(fⱼ∘kₗ)). This Lean 4 development proves that these traces do not generate all rational invariants of three frames, and that adjoining one…
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