Theorems · Definition · nonassociative algebras

LieIdeal.rootSpan

{K : Type u_1} →
  {L : Type u_2} →
    [inst : Field K] →
      [inst_1 : LieRing L] →
        [inst_2 : LieAlgebra K L] →
          [FiniteDimensional K L] →
            {H : LieSubalgebra K L} →
              [H.IsCartanSubalgebra] →
                [CharZero K] →
                  [LieAlgebra.IsKilling K L] →
                    [LieModule.IsTriangularizable K (↥H) L] → LieIdeal K L → Submodule K (Module.Dual K ↥H)

The submodule of Dual K H spanned by the roots associated to a Lie ideal.

Defined in

Mathlib.Algebra.Lie.Weights.IsSimple

Cited by

3 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLieRingLieAlgebraFiniteDimensionalLieSubalgebra.IsCartanSubalgebraCharZeroLieAlgebra.IsKillingLieModule.IsTriangularizable