isSl2Triple — Mathlib

English

The matrix e_i is nilpotent: some power e_i^n is the zero matrix.

Русский

Матрица e_i нильпотентна: существует n, что e_i^n = 0.

LaTeX

$$$e_i^n = 0$ for some n ∈ ℕ$$

Lean4

theorem isSl2Triple [DecidableEq ι] : IsSl2Triple (h i) (e i) (f i)
    where
  h_ne_zero := fun contra ↦ by simpa [h] using congr_fun₂ contra (.inr i) (.inr i)
  lie_e_f := by rw [lie_e_f_same]
  lie_h_e_nsmul := by rw [lie_h_e]; simp
  lie_h_f_nsmul := by rw [lie_h_f]; simp

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