Theorems · Theorem · nonassociative algebras

LieAlgebra.Extension.ringModuleOf_bracket

∀ {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] [inst_5 : IsLieAbelian M] (E : LieAlgebra.Extension R M L) (x : L)
  (y : M), ⁅x, y⁆ = E.toKer.symm ⁅Exists.choose ⋯ x, E.toKer y⁆

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

2 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebraIsLieAbelian