Theorems · Definition · nonassociative algebras

LieModule.IsRegular

(R : Type u_1) →
  {L : Type u_3} →
    (M : Type u_4) →
      [inst : CommRing R] →
        [inst_1 : LieRing L] →
          [inst_2 : LieAlgebra R L] →
            [Module.Finite R L] →
              [Module.Free R L] →
                [inst_5 : AddCommGroup M] →
                  [inst_6 : Module R M] →
                    [inst_7 : LieRingModule L M] →
                      [LieModule R L M] → [Module.Finite R M] → [Module.Free R M] → L → Prop

Let x be an element of a Lie algebra L over R, and write n for rank R L. Then x is regular if the n-th coefficient of the characteristic polynomial of ad R L x is non-zero.

Defined in

Mathlib.Algebra.Lie.Rank

Cited by

5 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraModule.FiniteModule.FreeAddCommGroupModuleLieRingModuleLieModuleModule.FiniteModule.Free