Theorems · Theorem · nonassociative algebras

LieAlgebra.IsKilling.corootSpace_eq_bot_iff

∀ {K : Type u_2} {L : Type u_3} [inst : LieRing L] [inst_1 : Field K] [inst_2 : LieAlgebra K L]
  [inst_3 : 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},
  LieAlgebra.corootSpace ⇑α = ⊥ ↔ α.IsZero

Defined in

Mathlib.Algebra.Lie.Weights.Killing

Cited by

0 results in Mathlib

Foundations

Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LieRingFieldLieAlgebraFiniteDimensionalLieSubalgebra.IsCartanSubalgebraLieAlgebra.IsKillingLieModule.IsTriangularizableCharZero