Theorems · Definition · nonassociative algebras

LieAlgebra.IsRegular

(R : Type u_1) →
  {L : Type u_3} →
    [inst : CommRing R] →
      [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → [Module.Finite R L] → [Module.Free R L] → 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

7 results in Mathlib

Foundations

Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraModule.FiniteModule.Free