Theorems · Theorem · nonassociative algebras

LieAlgebra.IsKilling.biSup_corootSubmodule_eq_cartan

∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [CharZero K] [inst_2 : LieRing L] [inst_3 : LieAlgebra K L]
  [LieAlgebra.IsKilling K L] [inst_5 : FiniteDimensional K L] (H : LieSubalgebra K L) [inst_6 : H.IsCartanSubalgebra]
  [LieModule.IsTriangularizable K (↥H) L],
  ⨆ α, ⨆ (_ : α.IsNonZero), LieAlgebra.IsKilling.corootSubmodule α = H.toLieSubmodule

Defined in

Mathlib.Algebra.Lie.Weights.RootSystem

Cited by

0 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldCharZeroLieRingLieAlgebraLieAlgebra.IsKillingFiniteDimensionalLieSubalgebra.IsCartanSubalgebraLieModule.IsTriangularizable