Theorems · Inductive type · nonassociative algebras

LieModule.IsTriangularizable

(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] → [LieModule R L M] → Prop

A Lie module M of a Lie algebra L is triangularizable if the endomorphism of M defined by any x : L is triangularizable.

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

125 results in Mathlib

Foundations

Depth 7 from the axioms, rests on 43 definitions · uses no axioms

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule