Theorems · Theorem · nonassociative algebras

LieAlgebra.rootSpaceProduct_tmul

∀ (R : Type u_1) (L : Type u_2) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  (H : LieSubalgebra R L) [inst_3 : LieRing.IsNilpotent ↥H] (χ₁ χ₂ χ₃ : ↥H → R) (hχ : χ₁ + χ₂ = χ₃)
  (x : ↥(LieAlgebra.rootSpace H χ₁)) (y : ↥(LieAlgebra.rootSpace H χ₂)),
  ↑((LieAlgebra.rootSpaceProduct R L H χ₁ χ₂ χ₃ hχ) (x ⊗ₜ[R] y)) = ⁅↑x, ↑y⁆

Defined in

Mathlib.Algebra.Lie.Weights.Cartan

Cited by

0 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRing.IsNilpotent