Theorems · Theorem · nonassociative algebras

LieSubmodule.lieIdeal_oper_eq_linear_span

∀ {R : Type u} {L : Type v} {M : Type w} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : AddCommGroup M]
  [inst_3 : Module R M] [inst_4 : LieRingModule L M] (N : LieSubmodule R L M) [inst_5 : LieAlgebra R L]
  (I : LieIdeal R L) [LieModule R L M], ↑⁅I, N⁆ = Submodule.span R {x | ∃ x_1 n, ⁅↑x_1, ↑n⁆ = x}

See also LieSubmodule.lieIdeal_oper_eq_linear_span' and LieSubmodule.lieIdeal_oper_eq_tensor_map_range.

Defined in

Mathlib.Algebra.Lie.IdealOperations

Cited by

9 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModuleLieAlgebraLieModule