Theorems · Definition · nonassociative algebras

LieAlgebra.IsKilling.reflectRoot

{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] →
              [FiniteDimensional K L] →
                {H : LieSubalgebra K L} →
                  [inst_6 : H.IsCartanSubalgebra] →
                    [LieModule.IsTriangularizable K (↥H) L] →
                      LieModule.Weight K (↥H) L → LieModule.Weight K (↥H) L → LieModule.Weight K (↥H) L

The reflection of a root along another.

Defined in

Mathlib.Algebra.Lie.Weights.RootSystem

Cited by

2 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldCharZeroLieRingLieAlgebraLieAlgebra.IsKillingFiniteDimensionalLieSubalgebra.IsCartanSubalgebraLieModule.IsTriangularizable