Theorems · Theorem · nonassociative algebras

LieAlgebra.Extension.toKer_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 : ↥E.proj.ker) (y : L), E.toKer ⁅y, E.toKer.symm x⁆ = ⁅Exists.choose ⋯ y, x⁆

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebraIsLieAbelian