Theorems · Theorem · nonassociative algebras

LieModule.genWeightSpace_chainTopCoeff_add_one_nsmul_add

∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] {M : Type u_3}
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [inst_6 : LieModule R L M]
  [inst_7 : LieRing.IsNilpotent L] [inst_8 : IsAddTorsionFree R] [inst_9 : IsDomain R]
  [inst_10 : Module.IsTorsionFree R M] [inst_11 : IsNoetherian R M] (α : L → R) (β : LieModule.Weight R L M),
  α ≠ 0 → LieModule.genWeightSpace M ((LieModule.chainTopCoeff α β + 1) • α + ⇑β) = ⊥

Defined in

Mathlib.Algebra.Lie.Weights.Chain

Cited by

6 results in Mathlib

Foundations

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

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotentIsAddTorsionFreeIsDomainModule.IsTorsionFreeIsNoetherian