Theorems · Theorem · nonassociative algebras

LieAlgebra.trace_toEnd_eq_zero

∀ {L : Type u_2} {M : Type u_3} [inst : LieRing L] [inst_1 : AddCommGroup M] [inst_2 : LieRingModule L M] {R : Type u_4}
  [inst_3 : CommRing R] [inst_4 : LieAlgebra R L] [inst_5 : Module R M] [inst_6 : LieModule R L M] {s : Set L},
  (∀ x ∈ s, (LinearMap.trace R M) ((LieModule.toEnd R L M) x) = 0) →
    ∀ {x : L}, x ∈ LieSubalgebra.lieSpan R L s → (LinearMap.trace R M) ((LieModule.toEnd R L M) x) = 0

Defined in

Mathlib.Algebra.Lie.Semisimple.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LieRingAddCommGroupLieRingModuleCommRingLieAlgebraModuleLieModule