Theorems · Theorem · nonassociative algebras

LieAlgebra.isKilling_of_equiv

∀ {R : Type u_1} {L : Type u_3} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] {L' : Type u_4}
  [inst_3 : LieRing L'] [inst_4 : LieAlgebra R L'] [LieAlgebra.IsKilling R L] (e : L ≃ₗ⁅R⁆ L'),
  LieAlgebra.IsKilling R L'

Given a Killing Lie algebra L, if L' is isomorphic to L, then L' is Killing too.

Defined in

Mathlib.Algebra.Lie.Killing

Cited by

1 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebraLieAlgebra.IsKilling