apply_lie_eq_add — Mathlib

English

If the Lie span of a set s is the whole Lie algebra, then two derivations that agree on s must be equal everywhere.

Русский

ЕслиLi-Span множества s равен всей Lie-алгебре, то две деривирования, совпадающие на s, равны на всей алгебре.

LaTeX

$$$\text{If } \operatorname{lieSpan}_R L s = \top, \text{ and } D_1|_s = D_2|_s, \text{ then } D_1 = D_2.$$$

Lean4

/-- For a Lie derivation from a Lie algebra to itself, the usual Leibniz rule holds. -/
theorem apply_lie_eq_add (D : LieDerivation R L L) (a b : L) : D ⁅a, b⁆ = ⁅a, D b⁆ + ⁅D a, b⁆ := by
  rw [LieDerivation.apply_lie_eq_sub, sub_eq_add_neg, lie_skew]

Похожие утверждения