Theorems · Theorem · nonassociative algebras

LieAlgebra.IsKilling.finrank_rootSpace_eq_one

∀ {K : Type u_2} {L : Type u_3} [inst : LieRing L] [inst_1 : Field K] [inst_2 : LieAlgebra K L] [FiniteDimensional K L]
  {H : LieSubalgebra K L} [inst_4 : H.IsCartanSubalgebra] [LieAlgebra.IsKilling K L]
  [LieModule.IsTriangularizable K (↥H) L] [CharZero K] (α : LieModule.Weight K (↥H) L),
  α.IsNonZero → Module.finrank K ↥(LieAlgebra.rootSpace H ⇑α) = 1

Defined in

Mathlib.Algebra.Lie.Weights.Killing

Cited by

6 results in Mathlib

Foundations

Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LieRingFieldLieAlgebraFiniteDimensionalLieSubalgebra.IsCartanSubalgebraLieAlgebra.IsKillingLieModule.IsTriangularizableCharZero