Theorems · Theorem · nonassociative algebras

LieModule.Weight.IsNonZero.neg

∀ {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] [inst_4 : LieAlgebra.IsKilling K L] {H : LieSubalgebra K L}
  [inst_5 : H.IsCartanSubalgebra] [inst_6 : LieModule.IsTriangularizable K (↥H) L] {α : LieModule.Weight K (↥H) L},
  α.IsNonZero → (-α).IsNonZero

Defined in

Mathlib.Algebra.Lie.Weights.Killing

Cited by

6 results in Mathlib

Foundations

Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LieRingFieldLieAlgebraFiniteDimensionalLieAlgebra.IsKillingLieSubalgebra.IsCartanSubalgebraLieModule.IsTriangularizable