Lie-algebra generation by a fixed Hodge operator and orthogonal actions

Do the fifteen orthogonal adjoint actions associated with diag(1,1,1,−1,1,−1), together with the local Hodge operator on coordinate plane 0123, generate sl(15,K) for every field of characteristic other than two?

Why it matters and what counts as progress

Why it matters: The specified generators provide a finite algebraic test of full Lie generation and rigidity across all characteristics other than two.

What counts as progress: Prove generation, dimension 224 and scalar rigidity of the commuting endomorphisms for this specified operator system.

How the problem developed

29 Sept 2026 · Formalized generation and rigidity theorem [1][2]
Stephanie Alexander, with OpenAI GPT-family agents; exact model revision not recorded Published a Lean development proving that a specified local Hodge operator and fifteen orthogonal adjoint actions generate sl(15,K) in characteristic other than two, with a scalar-commutant rigidity consequence.

AI contribution

AI-assisted proof establishes fixed Hodge Lie generation

For diag(1,1,1,−1,1,−1) and the local Hodge operator on coordinate plane 0123, fifteen orthogonal adjoint actions together with that operator generate sl(15,K) over every field of characteristic other than two. The same formal result gives dimension 224 and scalar rigidity for commuting endomorphisms, with determinant c²²⁴.

AI involvementAI-led

ImportanceModest

Technical verificationFormal (Lean 4.31.0 kernel and Comparator; exact integral commutator certificate)

Human understandingFew