`BookProof.ChapterGaugeAdjointAlgebra.adjVar_eq_zero_of_central` {X : L} (hX : ∀ θ : L, ⁅X, θ⁆ = 0) (θ : L) : adjVar θ X = 0

Proved

BookProof.ChapterGaugeAdjointAlgebra.adjVar_eq_zero_of_central

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeAdjointAlgebra.

BookProof.ChapterGaugeAdjointAlgebra.adjVar_eq_zero_of_central {X : L} (hX : ∀ θ : L, ⁅X, θ⁆ = 0) (θ : L) : adjVar θ X = 0

Formalization note: Lean 4 identifier BookProof.ChapterGaugeAdjointAlgebra.adjVar_eq_zero_of_central.

Preamble

-- Generated from ChapterGaugeAdjointAlgebra.lean — theorem BookProof.ChapterGaugeAdjointAlgebra.adjVar_eq_zero_of_central
import Mathlib
import Definitions.Def_ChapterGaugeAdjointAlgebra
open BookProof.ChapterGaugeAdjointAlgebra




open Finset

variable {L : Type*} [LieRing L]

Formal statement

theorem BookProof.ChapterGaugeAdjointAlgebra.adjVar_eq_zero_of_central {X : L} (hX : ∀ θ : L, ⁅X, θ⁆ = 0) (θ : L) :
    adjVar θ X = 0 := by sorry

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