Theorems · Theorem · nonassociative algebras

LieAlgebra.Extension.lie_toKer_apply

∀ {R : Type u_1} {L : Type u_3} {M : Type u_4} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : LieRing M] [inst_4 : LieAlgebra R M] (E : LieAlgebra.Extension R M L) (x : M) (y : E.L),
  ⁅y, ↑(E.toKer x)⁆ = ⁅y, E.incl x⁆

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra