Theorems · Definition · nonassociative algebras

LieAlgebra.IsKilling.coroot

{K : Type u_2} →
  {L : Type u_3} →
    [inst : LieRing L] →
      [inst_1 : Field K] →
        [inst_2 : LieAlgebra K L] →
          [FiniteDimensional K L] →
            {H : LieSubalgebra K L} →
              [inst_4 : H.IsCartanSubalgebra] → [LieAlgebra.IsKilling K L] → LieModule.Weight K (↥H) L → ↥H

The coroot corresponding to a root.

Defined in

Mathlib.Algebra.Lie.Weights.Killing

Cited by

34 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LieRingFieldLieAlgebraFiniteDimensionalLieSubalgebra.IsCartanSubalgebraLieAlgebra.IsKilling