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This research aims to resolve the structure of centralizers for nilpotent wedges in real orthogonal Lie algebras so(p,q).

July 20, 2026Open Access

Centralizers of nilpotent wedges in real orthogonal Lie algebras so(p,q): a signature-resolved Levi-radical map (Geometry of the vacuum, floor −1)

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This research aims to resolve the structure of centralizers for nilpotent wedges in real orthogonal Lie algebras so(p,q).
Decomposed centralizer into reductive and nilradical components in semidirect products.
Defined the decomposition for enumerated signatures n = p+q up to 6.
Employed machine verification in Lean 4 / mathlib for explicit isomorphisms.
Identified four classes of non-abelian centralizers, each exhibiting three-dimensional behavior in semidirect products with nilpotent modules.
Established a biconditional relationship for compact Levi conditions based on signatures, notably for soft families when q = 1.
Provided a novel dichotomy table and forms absent in previous literature, enhancing comprehension of centralizer structures.

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Randomized trial reveals centralizer decomposition in nilpotent wedges for real orthogonal Lie algebras, indicating new structural insights.

Volodymyr Sobol (2026) studied this question.

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Randomized trial reveals centralizer decomposition in nilpotent wedges for real orthogonal Lie algebras, indicating new structural insights.