Theorems · Definition · nonassociative algebras

LieSubalgebra.root

{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] → Finset (LieModule.Weight K (↥H) L)

The collection of roots as a Finset.

Defined in

Mathlib.Algebra.Lie.Weights.Killing

Cited by

34 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LieRingFieldLieAlgebraFiniteDimensionalLieSubalgebra.IsCartanSubalgebra