Theorems · Theorem · nonassociative algebras

LieAlgebra.killingForm_of_equiv_apply

∀ {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'] (e : L ≃ₗ⁅R⁆ L') (x y : L),
  ((killingForm R L') (e x)) (e y) = ((killingForm R L) x) y

Given an equivalence e of Lie algebras from L to L', and elements x y : L, the respective Killing forms of L and L' satisfy κ'(e x, e y) = κ(x, y).

Defined in

Mathlib.Algebra.Lie.Killing

Cited by

1 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra