Theorems · Theorem · nonassociative algebras

LieIdeal.mem_rootSet

∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : LieRing L] [inst_2 : LieAlgebra K L]
  [inst_3 : FiniteDimensional K L] {H : LieSubalgebra K L} [inst_4 : H.IsCartanSubalgebra] {I : LieIdeal K L}
  {α : ↥LieSubalgebra.root}, α ∈ I.rootSet ↔ LieAlgebra.rootSpace H ⇑↑α ≤ LieSubmodule.restr I H

Defined in

Mathlib.Algebra.Lie.Weights.IsSimple

Cited by

0 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLieRingLieAlgebraFiniteDimensionalLieSubalgebra.IsCartanSubalgebra