Theorems · Theorem · nonassociative algebras

LieAlgebra.IsKilling.root_apply_cartanEquivDual_symm_ne_zero

∀ {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]
  [inst_5 : LieAlgebra.IsKilling K L] [LieModule.IsTriangularizable K (↥H) L] [inst_7 : CharZero K]
  {α : LieModule.Weight K (↥H) L},
  α.IsNonZero → α ((LieAlgebra.IsKilling.cartanEquivDual H).symm (LieModule.Weight.toLinear K (↥H) L α)) ≠ 0

Defined in

Mathlib.Algebra.Lie.Weights.Killing

Cited by

4 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LieRingFieldLieAlgebraFiniteDimensionalLieSubalgebra.IsCartanSubalgebraLieAlgebra.IsKillingLieModule.IsTriangularizableCharZero