Theorems · Theorem · nonassociative algebras

LieAlgebra.Basis.iSupIndep_rootSpace

∀ {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} (b : LieAlgebra.Basis ι H) [inst_4 : Fintype ι] [IsDomain R]
  [CharZero R] [Module.IsTorsionFree R L],
  iSupIndep
    ![LieAlgebra.rootSpace H 0, ⨆ n, ⨆ (_ : n ≠ 0), LieAlgebra.rootSpace H (∑ i, n i • ⇑((-b.baseSupp) i)),
      ⨆ n, ⨆ (_ : n ≠ 0), LieAlgebra.rootSpace H (∑ i, n i • ⇑(b.baseSupp i))]

Defined in

Mathlib.Algebra.Lie.Basis.Basic

Cited by

3 results in Mathlib

Foundations

Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FiniteCommRingLieRingLieAlgebraFintypeIsDomainCharZeroModule.IsTorsionFree