Theorems · Theorem · nonassociative algebras

LieModule.IsTriangularizable.exists_hasEigenvalue

∀ (R : Type u_2) (L : Type u_3) (M : Type u_4) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [inst_6 : LieModule R L M] [Nontrivial M]
  [LieModule.IsTriangularizable R L M] (x : L), ∃ φ, ((LieModule.toEnd R L M) x).HasEigenvalue φ

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleNontrivialLieModule.IsTriangularizable