Theorems · Theorem · nonassociative algebras

LieModule.commute_toEnd_of_mem_center_left

∀ {R : Type u} {L : Type v} (M : Type w) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [inst_6 : LieModule R L M] {x : L},
  x ∈ LieAlgebra.center R L → ∀ (y : L), Commute ((LieModule.toEnd R L M) x) ((LieModule.toEnd R L M) y)

Defined in

Mathlib.Algebra.Lie.Abelian

Cited by

1 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule