Theorems · Theorem · nonassociative algebras

killingForm_apply_apply

∀ (R : Type u_1) (L : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (x y : L),
  ((killingForm R L) x) y = (LinearMap.trace R L) ((LieAlgebra.ad R L) x ∘ₗ (LieAlgebra.ad R L) y)

Defined in

Mathlib.Algebra.Lie.TraceForm

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebra