Theorems · Theorem · nonassociative algebras

LieIdeal.map_bracket_le

∀ {R : Type u} {L : Type v} {L' : Type w₂} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : LieRing L'] [inst_4 : LieAlgebra R L'] (f : L →ₗ⁅R⁆ L') {I₁ I₂ : LieIdeal R L},
  LieIdeal.map f ⁅I₁, I₂⁆ ≤ ⁅LieIdeal.map f I₁, LieIdeal.map f I₂⁆

Note that the inequality can be strict; e.g., the inclusion of an Abelian subalgebra of a simple algebra.

Defined in

Mathlib.Algebra.Lie.IdealOperations

Cited by

4 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra