Theorems · Definition · nonassociative algebras

LieAlgebra.Basis.baseSupp

{ι : Type u_1} →
  {R : Type u_2} →
    {L : Type u_3} →
      [inst : Finite ι] →
        [inst_1 : CommRing R] →
          [inst_2 : LieRing L] →
            [inst_3 : LieAlgebra R L] →
              {H : LieSubalgebra R L} → LieAlgebra.Basis ι H → [Fintype ι] → ι → Module.Dual R ↥H

These elements constitute a base for the root system of the Lie algebra relative to the associated Cartan subalgebra.

Defined in

Mathlib.Algebra.Lie.Basis.Basic

Cited by

15 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FiniteCommRingLieRingLieAlgebraFintype